Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

K-theory. --- Polytopes. --- Rings (Algebra). --- Polytopes --- K-theory --- Rings (Algebra) --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Algebraic rings --- Ring theory --- Mathematics. --- Algebra. --- Commutative algebra. --- Commutative rings. --- Convex geometry. --- Discrete geometry. --- Commutative Rings and Algebras. --- K-Theory. --- Convex and Discrete Geometry. --- Algebraic topology --- Homology theory --- Combinatorial geometry --- Algebra --- Mathematical analysis --- Math --- Science --- Algebraic fields --- Hyperspace --- Topology --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume collects contributions by leading experts in the area of commutative algebra related to the  INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to  June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.

Mathematics. --- Algebraic geometry. --- Category theory (Mathematics). --- Homological algebra. --- Commutative algebra. --- Commutative rings. --- Algebra. --- Field theory (Physics). --- Combinatorics. --- Commutative Rings and Algebras. --- Category Theory, Homological Algebra. --- Algebraic Geometry. --- Field Theory and Polynomials. --- Algebra --- Geometry, algebraic. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Combinatorics --- Mathematical analysis --- Algebraic geometry --- Geometry --- Mathematics --- Homological algebra --- Algebra, Abstract --- Homology theory --- Rings (Algebra) --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume collects contributions by leading experts in the area of commutative algebra related to the  INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to  June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.

Category theory. Homological algebra --- Ordered algebraic structures --- Algebra --- Algebraic geometry --- Geometry --- Discrete mathematics --- Classical mechanics. Field theory --- algebra --- landmeetkunde --- discrete wiskunde --- fysica --- mechanica --- geometrie