Monomial ideals and toric rings of Hibi type arising from a finite poset

In this paper we study monomial ideals attached to posets, introduce generalized Hibi rings and investigate their algebraic and homological properties. The main tools to study these objects are Grobner basis theory, the concept of sortability due to Sturmfels and the theory of weakly polymatroidal ideals.

[1]  Takayuki Hibi,et al.  Distributive Lattices, Bipartite Graphs and Alexander Duality , 2003 .

[2]  T. Hibi,et al.  Weakly Polymatroidal Ideals , 2006 .

[3]  Takayuki Hibi,et al.  Ideals of fiber type and polymatroids , 2005 .

[4]  H. Priestley,et al.  Distributive Lattices , 2004 .

[5]  D. Eisenbud,et al.  Cohen-Macaulay Rees Algebras and Their Specialization , 1983 .

[6]  Takayuki Hibi,et al.  Monomial ideals whose powers have a linear resolution , 2003 .

[7]  Monomial IdealsSerkan Ho.  Monomial Ideals , 2001 .

[8]  R. Fröberg,et al.  Koszul algebras, Veronese subrings, and rings with linear resolutions , 1985 .

[9]  Yukihide Takayama,et al.  Resolutions by mapping cones , 2001 .

[10]  Melvin Hochster,et al.  Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes , 1972 .

[11]  Takayuki Hibi,et al.  Distributive Lattices, Affine Semigroup Rings and Algebras with Straightening Laws , 1987 .

[12]  C. Huneke.  ON THE ASSOCIATED GRADED RING OF AN IDEAL , 1982 .

[13]  B. Sturmfels.  Gröbner bases and convex polytopes , 1995 .

[14]  Huy Tài Hà,et al.  Cohen-Macaulay admissible clutters , 2008, 0803.1332.

[15]  Edward L. Green,et al.  δ-Koszul Algebras , 2005 .

[16]  Richard P. Stanley,et al.  Balanced Cohen-Macaulay complexes , 1979 .

[17]  Rafael H. Villarreal,et al.  COHEN-MACAULAY, SHELLABLE AND UNMIXED CLUTTERS WITH A PERFECT MATCHING OF K ¨ , 2007, 0708.3111.

[18]  Victor Reiner,et al.  Resolutions of Stanley-Reisner rings and Alexander duality , 1998 .

[19]  J. Okninski,et al.  On monomial algebras , 1988, Semigroup Algebras.

[20]  Takayuki Hibi,et al.  The depth of powers of an ideal , 2004, math/0409178.