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Monomial algebras

Author: Rafael H Villarreal
Publisher: New York : M. Dekker, ©2001.
Series: Monographs and textbooks in pure and applied mathematics, 238.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Offers an introduction to the methods used to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings, and toric varieties. This title emphasizes square-free  Read more...

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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Rafael H Villarreal
ISBN: 0824705246 9780824705244
OCLC Number: 45202002
Description: ix, 455 p. : ill. ; 24 cm.
Contents: 1 Commutative Algebra 1 --
1.1 Module theory 1 --
1.2 Graded modules 12 --
1.3 Cohen-Macaulay modules 16 --
1.4 Normal rings 23 --
1.5 Koszul homology 28 --
2 Affine and Graded Algebras 31 --
2.1 Noether normalizations 31 --
2.2 Cohen-Macaulay graded algebras 35 --
2.3 Hilbert Nullstellensatz 45 --
2.4 Grobner bases 48 --
2.5 Minimal resolutions 58 --
3 Rees Algebras and Normality 65 --
3.1 Symmetric algebras 65 --
3.2 Rees algebras and syzygetic ideals 66 --
3.3 Complete and normal ideals 69 --
3.4 A criterion of Jurgen Herzog 82 --
3.5 Jacobian criterion 89 --
4 Hilbert Series 97 --
4.1 Hilbert-Serre's Theorem 97 --
4.2 a-invariants and h-vectors 106 --
4.3 Extremal algebras 110 --
4.4 Initial degrees of Gorenstein ideals 118 --
4.5 A symbolic study of Koszul homology 125 --
5 Monomial Ideals and Stanley-Reisner Rings 129 --
5.1 Primary decomposition 129 --
5.2 Simplicial complexes and homology 138 --
5.3 Face rings 142 --
5.4 Hilbert series of face rings 150 --
5.5 Upper bound conjectures 154 --
6 Edge Ideals 161 --
6.1 Graphs and ideals 161 --
6.2 Cohen-Macaulay graphs 172 --
6.3 Trees 178 --
6.4 Bipartite graphs 182 --
6.5 Links of some edge ideals 185 --
6.6 First syzygy module of an edge ideal 188 --
6.7 Edge rings with linear resolutions 192 --
7 Monomial Subrings 201 --
7.1 Basic properties 201 --
7.2 Integral closure of subrings 209 --
7.3 Integral closure of monomial ideals 233 --
7.4 Normality of some Rees algebras 239 --
7.5 Ideals of mixed products 248 --
7.6 Degree bounds for some integral closures 259 --
7.7 Degree bounds in the square-free case 261 --
7.8 Some lexicographical Grobner bases 276 --
8 Monomial Subrings of Graphs 281 --
8.1 Subring associated to a graph 282 --
8.2 Rees algebras of edge ideals 286 --
8.3 Incidence matrix of a graph 294 --
8.4 Circuits of a graph and Grobner bases 296 --
8.5 Edge subrings of bipartite planar graphs 303 --
8.6 Normality of bipartite graphs 311 --
8.7 Integral closure of an edge subring 315 --
8.8 Equations of the edge cone 325 --
9 Semigroup Rings of Complete Graphs 335 --
9.1 Monomial subrings of bipartite graphs 335 --
9.2 Monomial subrings of complete graphs 350 --
9.3 Noether normalizations of edge subrings 359 --
10 Monomial Curves 367 --
10.1 Defining equations of monomial curves 367 --
10.2 Symmetric semigroups 377 --
10.3 Ideals generated by critical binomials 385 --
10.4 An algorithm for critical binomials 399 --
11 Affine Toric Varieties and Toric Ideals 403 --
11.1 Systems of binomials in toric ideals 403 --
11.2 Affine toric varieties 409 --
11.3 Curves in positive characteristic 414 --
A Graph Diagrams 421 --
A.1 Cohen-Macaulay graphs 421 --
A.2 Unmixed graphs 424.
Series Title: Monographs and textbooks in pure and applied mathematics, 238.
Responsibility: Rafael H. Villarreal.
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." . .a swift overview. . .. . . .excellent. . .. . . .a thorough analysis." ---Mathematical Reviews ." . .graduate students and researchers. . .will find this volume very useful." ---Mathematica

 
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