The Cohomology Of Monoids

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The Cohomology of Monoids

Author : Antonio M. Cegarra
Publisher : Springer Nature
ISBN 13 : 3031502582
Total Pages : 227 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis The Cohomology of Monoids by : Antonio M. Cegarra

Download or read book The Cohomology of Monoids written by Antonio M. Cegarra and published by Springer Nature. This book was released on 2024 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general

The Cohomology of Commutative Semigroups

Author : Pierre Antoine Grillet
Publisher : Springer Nature
ISBN 13 : 3031082125
Total Pages : 191 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Cohomology of Commutative Semigroups by : Pierre Antoine Grillet

Download or read book The Cohomology of Commutative Semigroups written by Pierre Antoine Grillet and published by Springer Nature. This book was released on 2022-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years. The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification. Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.

Lectures on Logarithmic Algebraic Geometry

Author : Arthur Ogus
Publisher : Cambridge University Press
ISBN 13 : 1107187737
Total Pages : 559 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Lectures on Logarithmic Algebraic Geometry by : Arthur Ogus

Download or read book Lectures on Logarithmic Algebraic Geometry written by Arthur Ogus and published by Cambridge University Press. This book was released on 2018-11-08 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.

Operads: Proceedings of Renaissance Conferences

Author : Jean-Louis Loday
Publisher : American Mathematical Soc.
ISBN 13 : 0821805134
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operads: Proceedings of Renaissance Conferences by : Jean-Louis Loday

Download or read book Operads: Proceedings of Renaissance Conferences written by Jean-Louis Loday and published by American Mathematical Soc.. This book was released on 1997 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Algebra

Author : M. Hazewinkel
Publisher : Elsevier
ISBN 13 : 0080569412
Total Pages : 577 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Algebra by : M. Hazewinkel

Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2008-04-18 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

C.

Author : Saunders MacLane
Publisher : Springer Science & Business Media
ISBN 13 : 9783540586623
Total Pages : 444 pages
Book Rating : 4.5/5 (866 download)

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Book Synopsis C. by : Saunders MacLane

Download or read book C. written by Saunders MacLane and published by Springer Science & Business Media. This book was released on 1995-02-15 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Cohomology Theories for Compact Abelian Groups

Author : Karl H. Hofmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642806708
Total Pages : 235 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Cohomology Theories for Compact Abelian Groups by : Karl H. Hofmann

Download or read book Cohomology Theories for Compact Abelian Groups written by Karl H. Hofmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.

Linear Algebraic Monoids

Author : Lex E. Renner
Publisher : Springer Science & Business Media
ISBN 13 : 3540275568
Total Pages : 247 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Linear Algebraic Monoids by : Lex E. Renner

Download or read book Linear Algebraic Monoids written by Lex E. Renner and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

Commutative Semigroups

Author : P.A. Grillet
Publisher : Springer Science & Business Media
ISBN 13 : 1475733895
Total Pages : 443 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Commutative Semigroups by : P.A. Grillet

Download or read book Commutative Semigroups written by P.A. Grillet and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.

Calculus of Fractions and Homotopy Theory

Author : Peter Gabriel
Publisher : Springer Science & Business Media
ISBN 13 : 3642858449
Total Pages : 178 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Calculus of Fractions and Homotopy Theory by : Peter Gabriel

Download or read book Calculus of Fractions and Homotopy Theory written by Peter Gabriel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

Advances in Algebra

Author : K. P. Shum
Publisher : World Scientific
ISBN 13 : 9812382607
Total Pages : 531 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Advances in Algebra by : K. P. Shum

Download or read book Advances in Algebra written by K. P. Shum and published by World Scientific. This book was released on 2003 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R Gonchidorazh, former vice-president of the Mongolian Republic in Ulaanbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzzy algebras and applications.

Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry

Author : Stuart Margolis
Publisher : American Mathematical Society
ISBN 13 : 1470450429
Total Pages : 135 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry by : Stuart Margolis

Download or read book Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry written by Stuart Margolis and published by American Mathematical Society. This book was released on 2021-12-30 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids

Author : John Rhodes
Publisher : #N/A
ISBN 13 : 9814612715
Total Pages : 548 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids by : John Rhodes

Download or read book Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids written by John Rhodes and published by #N/A. This book was released on 1991-03-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the Berkeley Workshop on Monoids was to give expository talks by the most qualified experts in the emerging main areas of monoid and semigroup theory including applications to theoretical computer science. This was supplemented with current research papers. The topics covered, in an accessible way for the mathematical and theoretical computer community, were: Kernels and expansions in semigroup theory; Implicit operations; Inverse monoids; Varieties of semigroups and universal algebra; Linear semigroups and monoids of Lie type; Monoids acting on tress; Synthesis theorem, regular semigroups, and applications; Type-II conjecture; Application to theoretical computer science and decision problems.

Houston Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 638 pages
Book Rating : 4.:/5 (37 download)

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Book Synopsis Houston Journal of Mathematics by :

Download or read book Houston Journal of Mathematics written by and published by . This book was released on 1985 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Abelian Homological Algebra and Its Applications

Author : Hvedri Inassaridze
Publisher : Springer Science & Business Media
ISBN 13 : 9401588538
Total Pages : 268 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Non-Abelian Homological Algebra and Its Applications by : Hvedri Inassaridze

Download or read book Non-Abelian Homological Algebra and Its Applications written by Hvedri Inassaridze and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes methods of non-abelian homological algebra, such as the theory of satellites in abstract categories with respect to presheaves of categories and the theory of non-abelian derived functors of group valued functors. Applications to K-theory, bivariant K-theory and non-abelian homology of groups are given. The cohomology of algebraic theories and monoids are also investigated. The work is based on the recent work of the researchers at the A. Razmadze Mathematical Institute in Tbilisi, Georgia. Audience: This volume will be of interest to graduate students and researchers whose work involves category theory, homological algebra, algebraic K-theory, associative rings and algebras; algebraic topology, and algebraic geometry.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

Author : K. Glazek
Publisher : Springer Science & Business Media
ISBN 13 : 9401599645
Total Pages : 394 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by : K. Glazek

Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Homological Algebra (PMS-19), Volume 19

Author : Henry Cartan
Publisher : Princeton University Press
ISBN 13 : 1400883849
Total Pages : 408 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Homological Algebra (PMS-19), Volume 19 by : Henry Cartan

Download or read book Homological Algebra (PMS-19), Volume 19 written by Henry Cartan and published by Princeton University Press. This book was released on 2016-06-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.