This book examines interactions of polyhedral discrete geometry and algebra. What makes this book different from others is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory. The only prerequisite for the reader is a background in algebra. The basics of polyhedral geometry have been included as background material in Chapter 1. The text will be of interest to graduate students and mathematicians. Included are numerous exercises, historical background, and notes throughout the chapters. Examines interactions of polyhedral discrete geometry and algebra Presents seveal central results in all three areas of the expsition-from discrete geometry, commutative algebra, and K-theory Hasconstructive (i.e. algorithmic) nature at many places throughout the text Despite the large amount of information from various fields, the polytopal perspective is kept as the major organizational principle INDICE: 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.- Gröbner bases, triangulations, and Koszul algebras.- Projective modules over monoid rings.- Bass-Whitehead groups of monoid rings.- Varieties.- References.- Notation.- Index.
- ISBN: 978-0-387-76355-2
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 475
- Fecha Publicación: 01/07/2009
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- ÁLGEBRA