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＜電子ブック＞
Polytopes, Rings, and K-Theory / by Winfried Bruns, Joseph Gubeladze
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIV, 461 p. 52 illus : online resource
著者標目	*Bruns, Winfried author Gubeladze, Joseph author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Commutative algebra LCSH:Commutative rings LCSH:K-theory LCSH:Convex geometry  LCSH:Discrete geometry FREE:Algebra FREE:Commutative Rings and Algebras FREE:K-Theory FREE:Convex and Discrete Geometry
一般注記	I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University HTTP:URL=https://doi.org/10.1007/b105283

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