Gorenstein and Cohen–Macaulay matching complexes

A Numerical Characterization of Gorenstein Complexes

Let V be a finite set, called the vertex set, and let .1 be a simplicial complex on V. Thus .1 is a collection of subsets of V such that (i) {x} EL1 for any x E V, and (ii) a E .1, 'r c a imply 'r E L1. An element a of .1 is called an i-face if #( a) = i + 1. Here, #( a) is the cardinality of a as a set. The positive integer dim .1: = max{ #( a) 1; a E L1} is called the dimension of .1. Let v =...

Chessboard Complexes and Matching Complexes

Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

Unprojection theory analyzes and constructs complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes correspond to unprojections of type Kustin-Miller. As an application of our methods we study the minimal resolution of Stanley– Reisner rings associated to stacked po...

Homotopy category of projective complexes and complexes of Gorenstein projective modules

Let R be a ring with identity and C(R) denote the category of complexes of R-modules. In this paper we study the homotopy categories arising from projective (resp. injective) complexes as well as Gorenstein projective (resp. Gorenstein injective) modules. We show that the homotopy category of projective complexes over R, denoted K(Prj C(R)), is always well generated and is compactly generated p...

Gorenstein flat and Gorenstein injective dimensions of simple modules

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...