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Theory of Generalized Inverses Over Commutative Rings (Algebra, Logic and Applications)
K.P.S. Bhaskara Rao
Manufacturer: CRC
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ASIN: 0415272483 |
Book Description
The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative rings. Students, mathematicians working in g-inverses of matrices, along with algebraists, and control theorists will find new and indispensable data, presented with clarity and insight. This book is also well suited to graduate courses on g-inverses in algebra.
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Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics)
Patrice Tauvel , and
Rupert W.T. Yu
Manufacturer: Springer
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Elliptic Curves
ASIN: 3540241701 |
Book Description
The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Book Description
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.
Customer Reviews:
Coherent and Useful.......2006-07-25
This book does a good job at introducing some of the most interesting combinatorial problems in monomial resolutions. Although their chapter on toric varieties is somewhat weak, most of the other chapters (square-free monomial ideals, Borel-fixed ideals, staircases associated to monomial ideals in three variables, etc.) are very well written with challenging and revealing exercises at the end.
Book Description
This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time. Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials In Several Variables. For anyone interested in learning abstract algebra.
Customer Reviews:
Excellent Introduction To Algebra.......2006-03-21
Rotman's book is a standard for first courses in Abstract Algebra. The book is easy to read and includes plenty of problems to work on. He even includes several standard syllabi in the preface, depending on the type of course that may be taught with it. It begins with some number theory, then goes into the traditional group and ring concepts. The only reason I would say to not buy this book is if you really don't like the theorem-proof, theorem-proof kind of writing, but if you don't, you're likely not interested in Abstract Algebra anyway. An excellent book for learning as well as reference.
no better than the first edition.......2002-10-08
It is always easy to add something to than to get rid of something from the book. I guess this is the case of the author when he prepares the second edition. However, I prefer the first edition because it is more readable, enjoyable, and most importantly, contains just enough information for the introduction to abstract algebra. There are huge number of textbooks on abstract algbra, and making another would not be the author's purpose of the revision, I hope, but it looks it is.
By adding more subjects in detail to the second edition, now it looks the same as any other, only to loose its expository and conversational style of writings, and became a reference-style textbook.
Boo.......2001-03-27
Before taking an abstract algebra course this semester I studied the material on my own using the introductory texts by Gallian and Hungerford. These books were very useful because they actually completed proofs instead of leaving them as exercises for the reader. Someone new to abstract algebra is also typically new to higher mathematics. This means a book should have clear and full explanations, not skip major points like Rotman does. Rotman commits another sin by failing to provide homework problems which correspond with the material he presents. One nice thing is that the book does provide a wide array of material (much more than most other introductory texts). This virtue soon turns astray however because by providing so much preliminary material on congruences, functions, divisibility, .... you'll be lucky if your teacher gets to groups by halfway through the semester.
I'd skip this one..........2000-05-07
I was very disapointed with Rotman's attempt fix his first edition of this book. The wording is still overly dense, the topics skip around too much, and the examples are less than illuminating. At least he fixed the 10 by 10 orthogonal latin square on the cover to be correct this time. I think Hernstien's classic "Topics in Algebra" is a much better introduction
Excellent and aproacheable!.......1999-11-09
This is an excellent bookto use fo an introduction to modren algebra. It is clear and very accessible, with many useful examples. I highly recommend it.
Book Description
This is an English translation of the now classic "Algèbre Locale - Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.
Customer Reviews:
Serre as usual.......2005-11-02
This book is crystal clear and reads like a bedtime story. I wish I had it when I took commutative algebra.
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Ideals and Reality: Projective Modules and Number of Generators of Ideals (Springer Monographs in Mathematics)
Friedrich Ischebeck , and
Ravi A. Rao
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 3540230327 |
Book Description
This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1)$ hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratýnsk.
The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as
potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises.
Even this advanced material, presented comprehensively, keeps in mind the young student as potential reader besides the specialists of the subject.
Book Description
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.
Customer Reviews:
great text for graduate intro to comm. alg........2006-12-17
A great transition from elementary to advanced comm. ring theory: goes into greater details than Reid's Undergrad Comm. Alg. and Atiyah-MacDonald's Intro. to Comm. Alg. The proofs are clear and concise and the text is well-organized.
Truly Beautiful.......2000-04-28
Matsumura has achieved a great success with this book. The first nine chapters contain all of the algebra used in Hartshorne's _Algebraic Geometry_, and a reader who masters all of that material will be well on the way to a solid understanding of algebraic geometry. At the same time, the writing is clear and concise, and the exercises (which the reader should of course do!) are enlightening. In this regard, one should compare Matsumura's book with Eisenbud's _Commutative Algebra with a View Toward Algebraic Geometry_, which has a similar scope but takes up 800 pages. Both books are beautifully written, but while Matsumura prefers a more subtle way of teaching the reader the tricks of the trade, Eisenbud makes explicit commentary on his methods and intuition. Another helpful comparison between the two is in their fundamental approach: Matsumura tends to use universal constructions which are not computationally effective, while Eisenbud seems to keep the computer in mind. Thus, whereas Eisenbud studies the module of differentials using generators and relations, Matsumura uses the universal properties of representable functors.
Unfortunately, this book is not sufficient for a first introduction to commutative algebra, as the pace can be brisk for a reader without the mathematical maturity to appreciate Matsumura's condensed style. (One could read this book after reading Atiyah and MacDonald's _Introduction to Commutative Algebra_.) Nevertheless, for a reader seeking a solid understanding of the commutative algebra necessary for (modern) algebraic geometry, there is no better reference than Matsumura's book.
A minor gripe: the formatting is visually slightly confusing -- the announcements of Theorems, Corollaries, Lemmas, Remarks, Proofs, etc. are all set in italic typeface, so there is not much to orient the eye on the page.
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Polynomial Identity Rings (Advanced Courses in Mathematics - CRM Barcelona)
Vesselin Drensky , and
Edward Formanek
Manufacturer: Birkhäuser Basel
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Computational Aspects of Polynomial Identities (Research Notes in Mathematics)
ASIN: 3764371269 |
Book Description
A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity.
These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity.
The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.
The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.
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Advances in Commutative Ring Theory (Lecture Notes in Pure and Applied Mathematics)
Manufacturer: CRC
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Binding: Paperback
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ASIN: 0824771478 |
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"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
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