Some Aspects Of Ring Theory
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Author | : Paul M. Cohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 234 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1447104757 |
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.
Author | : I. N. Herstein |
Publisher | : |
Total Pages | : 254 |
Release | : 2011-03-30 |
Genre | : |
ISBN | : 9783642110375 |
Author | : I. N. Herstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 252 |
Release | : 2011-06-01 |
Genre | : Mathematics |
ISBN | : 3642110363 |
S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in local ring theory.- P.H. Cohn: Two topics in ring theory.- A.W. Goldie: Non-commutative localisation.
Author | : |
Publisher | : |
Total Pages | : 246 |
Release | : 1965 |
Genre | : Rings (Mathematics). |
ISBN | : |
Author | : Nathan Jacobson |
Publisher | : American Mathematical Soc. |
Total Pages | : 160 |
Release | : 1943-12-31 |
Genre | : Mathematics |
ISBN | : 0821815024 |
The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
Author | : C. Nastasescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 1987-04-30 |
Genre | : Mathematics |
ISBN | : 9789027724618 |
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.
Author | : Centro internazionale matematico estivo |
Publisher | : |
Total Pages | : 246 |
Release | : 1966 |
Genre | : |
ISBN | : |
Author | : I. N. Herstein |
Publisher | : |
Total Pages | : 156 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : |
Author | : Paolo Aluffi |
Publisher | : American Mathematical Soc. |
Total Pages | : 713 |
Release | : 2021-11-09 |
Genre | : Education |
ISBN | : 147046571X |
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475739877 |
Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.