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Trends In Commutative Algebra
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Book Synopsis Trends in Commutative Algebra by : Luchezar L. Avramov
Download or read book Trends in Commutative Algebra written by Luchezar L. Avramov and published by Cambridge University Press. This book was released on 2004-12-13 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology, and combinatorics.
Book Synopsis Trends in Commutative Rings Research by : Ayman Badawi
Download or read book Trends in Commutative Rings Research written by Ayman Badawi and published by Nova Publishers. This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trends in Commutative Rings Research
Book Synopsis Progress in Commutative Algebra 1 by : Christopher Francisco
Download or read book Progress in Commutative Algebra 1 written by Christopher Francisco and published by Walter de Gruyter. This book was released on 2012-04-26 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.
Book Synopsis Progress in Commutative Algebra 2 by : Christopher Francisco
Download or read book Progress in Commutative Algebra 2 written by Christopher Francisco and published by Walter de Gruyter. This book was released on 2012-04-26 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.
Book Synopsis Advances in Commutative Algebra by : Ayman Badawi
Download or read book Advances in Commutative Algebra written by Ayman Badawi and published by Springer. This book was released on 2019-04-11 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the contributions of the eminent mathematician and leading algebraist David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of topics for experts and non-experts, with a mix of survey papers to offer a synopsis of developments across a range of areas of commutative algebra and outlining Anderson’s work. The book is divided into two sections—surveys and recent research developments—with each section presenting material from all the major areas in commutative algebra. The book is of interest to graduate students and experienced researchers alike.
Book Synopsis Progress in Commutative Algebra 1 by : Christopher Francisco
Download or read book Progress in Commutative Algebra 1 written by Christopher Francisco and published by . This book was released on 2012-04-26 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biographical note: Christopher Francisco, Oklahoma State University, Stillwater, Oklahoma, USA; Lee C. Klingler, Florida Atlantic University, Boca Raton, Florida, USA; Sean M. Sather-Wagstaff, North Dakota State University, Fargo, North Dakota, USA; Janet Vassilev, University of New Mexico, Albuquerque, New Mexico, USA.
Book Synopsis Progress in commutative algebra by : Sean Sather-Wagstaff
Download or read book Progress in commutative algebra written by Sean Sather-Wagstaff and published by Walter de Gruyter. This book was released on 2012-04-13 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions atthe 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.
Book Synopsis Commutative Ring Theory and Applications by : Marco Fontana
Download or read book Commutative Ring Theory and Applications written by Marco Fontana and published by CRC Press. This book was released on 2017-07-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome
Book Synopsis Commutative Algebra by : Melvin Hochster
Download or read book Commutative Algebra written by Melvin Hochster and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.
Book Synopsis Progress in commutative algebra: Closures, finiteness, and factorization by : Sean Sather-Wagstaff
Download or read book Progress in commutative algebra: Closures, finiteness, and factorization written by Sean Sather-Wagstaff and published by Walter de Gruyter. This book was released on 2012 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions atthe 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.
Book Synopsis Algebra. Some Current Trends by : Luchezar L. Avramov
Download or read book Algebra. Some Current Trends written by Luchezar L. Avramov and published by . This book was released on 2014-01-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller
Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah
Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Book Synopsis Trends in Representation Theory of Algebras and Related Topics by : Andrzej Skowroński
Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Book Synopsis Computational Commutative and Non-commutative Algebraic Geometry by : Svetlana Cojocaru
Download or read book Computational Commutative and Non-commutative Algebraic Geometry written by Svetlana Cojocaru and published by . This book was released on 2005 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of inf.
Download or read book Monomial Ideals written by Jürgen Herzog and published by Springer Science & Business Media. This book was released on 2010-09-28 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.
Book Synopsis Ring and Module Theory by : Toma Albu
Download or read book Ring and Module Theory written by Toma Albu and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
