Polytopes, Rings, and K-Theory [Paperback]

This 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.

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.

From the reviews:

The book deals with the convex geometry of the polyhedral cones CM and related topics & . With an extensive list of references together with historical notes at the end of each chapter, this book will serve as a welcome comprehensive monograph for research on these rich and fascinating subjects. (T. Oda, Mathematical Reviews, Issue 2010 d)

Interactions between convex geometry, ring theory, K-theory, combinatorial geometry, toric geometry, combinatorics in commutative algebra, which are presented in this book together with & central results in each of the above fields. & All the chapters contain many useful exercises & . a good part of the book is not covered by any other book and so especially people from commutative algebra should have it. (Dorin-Mihail Popescu, Zentralblatt MATH, Vol. 1168, 2009)

Polytopes, Rings, and K-Theory weighs in at over 400 pages and ten chapters split into three main parts, culminating in the aforementioned K-theory in the given context. & There are exercises galore in the book & . All in all, Polytopes, Rings, and K-Theory is an accessible and well-written book on an interesting and important subject & . It should be quite a success. (Michael Berg, ThelC!