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Cyclic Galois Extensions Of Commutative Rings
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Book Synopsis Cyclic Galois Extensions of Commutative Rings by : Cornelius Greither
Download or read book Cyclic Galois Extensions of Commutative Rings written by Cornelius Greither and published by Springer. This book was released on 2006-11-15 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.
Book Synopsis Varieties of Lattices by : Peter Jipsen
Download or read book Varieties of Lattices written by Peter Jipsen and published by Springer. This book was released on 1992-12-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.
Book Synopsis Linear and Complex Analysis Problem Book 3 by : Victor P. Havin
Download or read book Linear and Complex Analysis Problem Book 3 written by Victor P. Havin and published by Springer. This book was released on 1994-04-28 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
Book Synopsis The Separable Galois Theory of Commutative Rings by : Andy R. Magid
Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a n
Book Synopsis Separable Algebras by : Timothy J. Ford
Download or read book Separable Algebras written by Timothy J. Ford and published by American Mathematical Soc.. This book was released on 2017-09-26 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Book Synopsis Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups by : John Rognes
Download or read book Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups written by John Rognes and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Book Synopsis Number Theory by : Jean-Marie De Koninck
Download or read book Number Theory written by Jean-Marie De Koninck and published by Walter de Gruyter. This book was released on 1989 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monumental proceedings (very handsomely produced) of a major international conference. The book contains 74 refereed articles which, apart from a few survey papers of peculiar interest, are mostly research papers (63 in English, 11 in French). The topics covered reflect the full diversity of the current trends and activities in modern number theory: elementary, algebraic and analytic number theory; constructive (computational) number theory; elliptic curves and modular forms; arithmetical geometry; transcendence; quadratic forms; coding theory. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Ecole D'ete de Probabilites de Saint-Flour by : J. Bertoin
Download or read book Ecole D'ete de Probabilites de Saint-Flour written by J. Bertoin and published by Springer Science & Business Media. This book was released on 1999-11-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.
Book Synopsis Galois Theory and Cohomology of Commutative Rings by : Stephen Urban Chase
Download or read book Galois Theory and Cohomology of Commutative Rings written by Stephen Urban Chase and published by . This book was released on 1968 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir consists of three related papers. In the first paper, the main theorems of Galois theory for fields are generalized to commutative rings. In the second paper B(S/R) is described cohomologically. In the third paper the set of all Galois extensions of a commutative ring with a given Abelian Galois group is shown to be a group.
Book Synopsis Generic Polynomials by : Christian U. Jensen
Download or read book Generic Polynomials written by Christian U. Jensen and published by Cambridge University Press. This book was released on 2002-12-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Cyclic Galois extensions and normal bases by : Cornelius Greither
Download or read book Cyclic Galois extensions and normal bases written by Cornelius Greither and published by . This book was released on 1988 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hokkaido Mathematical Journal written by and published by . This book was released on 1998 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Theory and Cohomology of Commutative Rings by : Stephen Urban Chase
Download or read book Galois Theory and Cohomology of Commutative Rings written by Stephen Urban Chase and published by American Mathematical Soc.. This book was released on 1969 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Separable Galois Theory of Commutative Rings by : Andy Roy Magid
Download or read book The Separable Galois Theory of Commutative Rings written by Andy Roy Magid and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Skew Fields written by Paul Moritz Cohn and published by Cambridge University Press. This book was released on 1995-07-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-commutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts and most accounts have hitherto been confined to division algebras, that is skew fields finite-dimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation and a precise description of the embedding problem are followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorems of G. M. Bergman are proved here as well as the properties of the matrix reduction functor, a useful but little-known construction providing a source of examples and counter-examples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of non-commutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background.
Book Synopsis The Problem of Catalan by : Yuri F. Bilu
Download or read book The Problem of Catalan written by Yuri F. Bilu and published by Springer. This book was released on 2014-10-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 – 23 = 1 is the only solution of the equation xp – yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2. In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
Book Synopsis Finite Commutative Rings and Their Applications by : Gilberto Bini
Download or read book Finite Commutative Rings and Their Applications written by Gilberto Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.
