Abstract Algebraic Closure Operations and Instructions in Ring Theory PDF Download
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Author: Peter Malcolmson
Publisher:
ISBN:
Category :
Languages : en
Pages : 176
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Book Description
Author: Peter Malcolmson
Publisher:
ISBN:
Category :
Languages : en
Pages : 176
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Book Description
Author: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 0387005005
Category : Mathematics
Languages : en
Pages : 369
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Book Description
" This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the 'tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. " (T. W. Hungerford, Mathematical Reviews)
Author: Jesse Elliott
Publisher: Springer Nature
ISBN: 3030244016
Category : Mathematics
Languages : en
Pages : 490
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Book Description
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Author: Fernando Q. Gouvêa
Publisher: MAA
ISBN: 0883853558
Category : Mathematics
Languages : en
Pages : 329
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Book Description
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
Author: Golan
Publisher: CRC Press
ISBN: 1351430378
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
Author: Daniel G. Coronell
Publisher: CRC Press
ISBN: 1584885157
Category : Science
Languages : en
Pages : 693
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Book Description
Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.
Author: Kaiming Zhao
Publisher: World Scientific
ISBN: 9811255792
Category : Mathematics
Languages : en
Pages : 198
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Book Description
This book is intended as a textbook for a one-term senior undergraduate (or graduate) course in Ring and Field Theory, or Galois theory. The book is ready for an instructor to pick up to teach without making any preparations.The book is written in a way that is easy to understand, simple and concise with simple historic remarks to show the beauty of algebraic results and algebraic methods. The book contains 240 carefully selected exercise questions of varying difficulty which will allow students to practice their own computational and proof-writing skills. Sample solutions to some exercise questions are provided, from which students can learn to approach and write their own solutions and proofs. Besides standard ones, some of the exercises are new and very interesting. The book contains several simple-to-use irreducibility criteria for rational polynomials which are not in any such textbook.This book can also serve as a reference for professional mathematicians. In particular, it will be a nice book for PhD students to prepare their qualification exams.
Author: Peter Malcolmson
Publisher:
ISBN:
Category :
Languages : en
Pages : 192
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Book Description
Author: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 1468404067
Category : Mathematics
Languages : en
Pages : 410
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Book Description
One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.
Author: I. N. Herstein
Publisher: Literary Licensing, LLC
ISBN:
Category : Literary Collections
Languages : en
Pages : 138
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Book Description
Theory of Rings is a comprehensive textbook on abstract algebra, specifically focusing on the theory of rings, written by Israel Nathan Herstein. The book covers a wide range of topics, including the structure of rings, modules, homomorphisms, ideals, polynomial rings, and field theory. The author provides clear and concise explanations of each concept, accompanied by numerous examples and exercises to help readers understand and apply the material. The book is intended for advanced undergraduate and graduate students in mathematics, as well as researchers and professionals in the field. With its rigorous and detailed treatment of the subject matter, Theory of Rings is an essential resource for anyone interested in the theory of rings and its applications.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
