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Introduction to Ring Theory

Introduction to Ring Theory PDF Author: Paul M. Cohn
Publisher: Springer Science & Business Media
ISBN: 1447104757
Category : Mathematics
Languages : en
Pages : 234

Book Description
A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.

Introduction to Ring Theory

Introduction to Ring Theory PDF Author: Paul M. Cohn
Publisher: Springer Science & Business Media
ISBN: 1447104757
Category : Mathematics
Languages : en
Pages : 234

Book Description
A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.

Ring Theory And Algebraic Geometry

Ring Theory And Algebraic Geometry PDF Author: A. Granja
Publisher: CRC Press
ISBN: 9780203907962
Category : Mathematics
Languages : en
Pages : 366

Book Description
Focuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and binomial ideals, cones and fans, affine and projective algebraic varieties, simplicial and cellular complexes, polytopes, and arithmetics.

Rings, Fields, and Vector Spaces

Rings, Fields, and Vector Spaces PDF Author: Bharath Sethuraman
Publisher: Springer Science & Business Media
ISBN: 0387948481
Category : Mathematics
Languages : en
Pages : 210

Book Description
Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.

Ring and Module Theory

Ring and Module Theory PDF Author: Toma Albu
Publisher: Springer Science & Business Media
ISBN: 3034600070
Category : Mathematics
Languages : en
Pages : 204

Book Description
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.

Dimensions of Ring Theory

Dimensions of Ring Theory PDF Author: C. Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9789027724618
Category : Mathematics
Languages : en
Pages : 382

Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Undergraduate Commutative Algebra

Undergraduate Commutative Algebra PDF Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521458894
Category : Mathematics
Languages : en
Pages : 172

Book Description
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.

Commutative Ring Theory

Commutative Ring Theory PDF Author: Hideyuki Matsumura
Publisher: Cambridge University Press
ISBN: 9780521367646
Category : Mathematics
Languages : en
Pages : 338

Book Description
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Introduction To Commutative Algebra

Introduction To Commutative Algebra PDF Author: Michael F. Atiyah
Publisher: CRC Press
ISBN: 0429973268
Category : Mathematics
Languages : en
Pages : 140

Book Description
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.

Polytopes, Rings, and K-Theory

Polytopes, Rings, and K-Theory PDF Author: Winfried Bruns
Publisher: Springer Science & Business Media
ISBN: 0387763562
Category : Mathematics
Languages : en
Pages : 461

Book Description
This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.

Cox Rings

Cox Rings PDF Author: Ivan Arzhantsev
Publisher: Cambridge University Press
ISBN: 1107024625
Category : Mathematics
Languages : en
Pages : 539

Book Description
This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.