TY - BOOK ID - 7765244 TI - Polytopes, rings, and K-theory AU - Bruns, Winfried. AU - Gubeladze, Joseph. PY - 2009 SN - 1441926178 0387763554 9786612292149 1282292145 0387763562 PB - Dordrecht ; London : Springer, DB - UniCat KW - K-theory. KW - Polytopes. KW - Rings (Algebra). KW - Polytopes KW - K-theory KW - Rings (Algebra) KW - Geometry KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebraic rings KW - Ring theory KW - Mathematics. KW - Algebra. KW - Commutative algebra. KW - Commutative rings. KW - Convex geometry. KW - Discrete geometry. KW - Commutative Rings and Algebras. KW - K-Theory. KW - Convex and Discrete Geometry. KW - Algebraic topology KW - Homology theory KW - Combinatorial geometry KW - Algebra KW - Mathematical analysis KW - Math KW - Science KW - Algebraic fields KW - Hyperspace KW - Topology KW - Discrete groups. KW - Groups, Discrete KW - Infinite groups KW - Discrete mathematics KW - Convex geometry . UR - https://www.unicat.be/uniCat?func=search&query=sysid:7765244 AB - 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. ER -