K-theory, Projective Modules, and Complete Intersections
Author: Benjamin Parker Nicholson
Publisher:
Published: 1998
Total Pages: 94
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Benjamin Parker Nicholson
Publisher:
Published: 1998
Total Pages: 94
ISBN-13:
DOWNLOAD EBOOKAuthor: Satya Mandal
Publisher: Springer
Published: 2006-11-14
Total Pages: 121
ISBN-13: 3540695982
DOWNLOAD EBOOKIn 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: Friedrich Ischebeck
Publisher: Springer Science & Business Media
Published: 2005-11-22
Total Pages: 339
ISBN-13: 3540263705
DOWNLOAD EBOOKBesides 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: A. J. Berrick
Publisher: Cambridge University Press
Published: 2000-05-25
Total Pages: 384
ISBN-13: 9780521632768
DOWNLOAD EBOOKThis book, first published in 2000, is a concise introduction at graduate level to ring theory, module theory and number theory.
Author: Vasudevan Srinivas
Publisher: Springer Science & Business Media
Published: 2009-05-21
Total Pages: 357
ISBN-13: 0817647392
DOWNLOAD EBOOKAlgebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
Author: A. A. Ambily
Publisher: Springer Nature
Published: 2020-01-17
Total Pages: 340
ISBN-13: 9811516111
DOWNLOAD EBOOKThe 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: Winfried Bruns
Publisher: Springer Science & Business Media
Published: 2009-06-12
Total Pages: 461
ISBN-13: 0387763562
DOWNLOAD EBOOKThis book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
Author: Jonathan Rosenberg
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 404
ISBN-13: 1461243149
DOWNLOAD EBOOKAlgebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Author: David Eisenbud
Publisher: Springer
Published: 2016-03-08
Total Pages: 113
ISBN-13: 3319264370
DOWNLOAD EBOOKThis book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.
Author: Charles A. Weibel
Publisher: American Mathematical Soc.
Published: 2013-06-13
Total Pages: 634
ISBN-13: 0821891324
DOWNLOAD EBOOKInformally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr