Lessons on Rings, Modules and Multiplicities

by D. G. Northcott
Lessons on Rings, Modules and Multiplicities
Author: D. G. Northcott
Publisher:
Total Pages: 472
Release: 2008-12-11
Genre: Mathematics
ISBN:
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This volume provides a clear and self-contained introduction to important results in the theory of rings and modules. Assuming only the mathematical background provided by a normal undergraduate curriculum, the theory is derived by comparatively direct and simple methods. It will be useful to both undergraduates and research students specialising in algebra. In his usual lucid style the author introduces the reader to advanced topics in a manner which makes them both interesting and easy to assimilate. As the text gives very full explanations, a number of well-ordered exercises are included at the end of each chapter. These lead on to further significant results and give the reader an opportunity to devise his own arguments and to test his understanding of the subject.

Rings, Modules, Algebras, and Abelian Groups

by Alberto Facchini
Rings, Modules, Algebras, and Abelian Groups
Author: Alberto Facchini
Publisher: CRC Press
Total Pages: 530
Release: 2020-02-10
Genre: Mathematics
ISBN: 9780824750817
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Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological

Advances in Rings, Modules and Factorizations

by Alberto Facchini
Advances in Rings, Modules and Factorizations
Author: Alberto Facchini
Publisher: Springer Nature
Total Pages: 341
Release: 2020-06-02
Genre: Mathematics
ISBN: 3030434168
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Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

Algebras, Rings and Modules

by Michiel Hazewinkel
Algebras, Rings and Modules
Author: Michiel Hazewinkel
Publisher: CRC Press
Total Pages: 384
Release: 2016-04-05
Genre: Mathematics
ISBN: 1482245051
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The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu

A First Course of Homological Algebra

by Douglas Geoffrey Northcott
A First Course of Homological Algebra
Author: Douglas Geoffrey Northcott
Publisher: CUP Archive
Total Pages: 224
Release: 1973-10-11
Genre: Mathematics
ISBN: 9780521201964
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Designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject.

Computational Algebraic Geometry

by Frederic Eyssette
Computational Algebraic Geometry
Author: Frederic Eyssette
Publisher: Springer Science & Business Media
Total Pages: 334
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461227526
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The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J.H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H.M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J.J.

Effective Methods in Algebraic Geometry

by T. Mora
Effective Methods in Algebraic Geometry
Author: T. Mora
Publisher: Springer Science & Business Media
Total Pages: 504
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461204410
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The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").

Arrangements of Hyperplanes

by Peter Orlik
Arrangements of Hyperplanes
Author: Peter Orlik
Publisher: Springer Science & Business Media
Total Pages: 337
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662027720
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An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.