Serre's Problem on Projective Modules PDF Download

Author: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 3540345752
Category : Mathematics
Languages : en
Pages : 412

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An invaluable summary of research work done in the period from 1978 to the present

Author: Friedrich Ischebeck
Publisher: Springer Science & Business Media
ISBN: 3540263705
Category : Mathematics
Languages : en
Pages : 339

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Book Description
Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

Author: Satya Mandal
Publisher: Springer
ISBN: 3540695982
Category : Mathematics
Languages : en
Pages : 121

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Book Description
In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions." These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.

Author: T.Y. Lam
Publisher: Springer
ISBN: 3540359265
Category : Mathematics
Languages : en
Pages : 240

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From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre's Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical 'guided tour'. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the 'guide' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way."

Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446

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Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Author: Ivan Matveevich Vinogradov
Publisher: American Mathematical Soc.
ISBN: 9780821830963
Category : Algebra
Languages : en
Pages : 284

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Book Description
Collection of papers on the current research in algebra, mathematical logic, number theory and topology.

Author: A. A. Ambily
Publisher: Springer Nature
ISBN: 9811516111
Category : Mathematics
Languages : en
Pages : 340

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Book Description
The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

Author: D. Handelman
Publisher: Springer
ISBN: 3540350438
Category : Mathematics
Languages : en
Pages : 361

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Book Description
A ring theory conference took place at the University of Waterloo, 12-16 June 1978, and these are its proceedings. This conference was held as a part of the Summer Research Institute in Ring Theory, at Waterloo, sponsored by the Canadian Mathematical Society. In soliciting speakers, and contributors to the Proceedings, we attempted to represent those portions of ring theory which seemed to us interesting. There was thus considerable emphasis on lower K-theory and related topics, Artinian and Noetherian rings, as well as actions and representations of groups on rings. Regrettably, we could only obtain one paper in the mainstream of commutative ring theory, but we believe that the lack of quantity is more than made up for by the quality. We also took the liberty of including a survey of results in a field which we feel deserves more attention by ring theorists, C* algebras from an algebraic point of view.

Author: J. C. Misra
Publisher: Alpha Science Int'l Ltd.
ISBN: 9788173194870
Category : Mathematics
Languages : en
Pages : 528

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Book Description
This comprehensive volume introduces educational units dealing with the various emerging branches of Applicable Mathematics. It consists of chapters that deal with the major areas of pure mathematics and emphasises the cross-field application of the skills conveyed within.

Author: Robin Hartshorne
Publisher: American Mathematical Soc.
ISBN: 082181429X
Category : Mathematics
Languages : en
Pages : 658

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Book Description