Serre S Problem On Projective Modules
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Serre S Problem On Projective Modules
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-17
Serre S Problem On Projective Modules written by T.Y. Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.
An invaluable summary of research work done in the period from 1978 to the present
Ideals And Reality
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Author : Friedrich Ischebeck
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-22
Ideals And Reality written by Friedrich Ischebeck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-22 with Mathematics categories.
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,. . .
Projective Modules And Serre S Conjecture
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Author : Michael P. Whalen
language : en
Publisher:
Release Date : 1977
Projective Modules And Serre S Conjecture written by Michael P. Whalen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Serre S Conjecture
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Author : T.Y. Lam
language : en
Publisher: Springer
Release Date : 2006-11-15
Serre S Conjecture written by T.Y. Lam and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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."
Leavitt Path Algebras And Classical K Theory
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Author : A. A. Ambily
language : en
Publisher: Springer Nature
Release Date : 2020-01-17
Leavitt Path Algebras And Classical K Theory written by A. A. Ambily and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-17 with Mathematics categories.
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.
Commutative Algebra Constructive Methods
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Author : Henri Lombardi
language : en
Publisher: Springer
Release Date : 2015-07-22
Commutative Algebra Constructive Methods written by Henri Lombardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.
Algebra K Theory Groups And Education
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Author : Hyman Bass
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebra K Theory Groups And Education written by Hyman Bass and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.
Algebra Mathematical Logic Number Theory Topology
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Author : Ivan Matveevich Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Algebra Mathematical Logic Number Theory Topology written by Ivan Matveevich Vinogradov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Algebra categories.
Collection of papers on the current research in algebra, mathematical logic, number theory and topology.
Ring Theory Waterloo 1978
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Author : D. Handelman
language : en
Publisher: Springer
Release Date : 2007-01-05
Ring Theory Waterloo 1978 written by D. Handelman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
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.
Algebraic Geometry Arcata 1974
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Author : Robin Hartshorne
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
Algebraic Geometry Arcata 1974 written by Robin Hartshorne and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Mathematics categories.