Polytopes, Rings, and K-Theory

• Main Authors: Gubeladze, Joseph. (Author), Bruns, Winfried. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Edition: 1.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; K-theory.; Discrete groups.; Convex and Discrete Geometry.; K-Theory.; Commutative Rings and Algebras.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/b105283

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 severa...

Table of Contents:

• Preface
• Polytopes, cones, and complexes
• Affine monoids and their Hilbert bases
• Multiples of lattice polytopes
• Monoid algebras
• Isomorphisms and automorphisms
• Homological properties and Hilbert functions
• Grb̲ner bases, triangulations, and Koszul algebras
• Projective modules over monoid rings
• Bass-Whitehead groups of monoid rings
• Varieties
• References
• Notation
• Index.