Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/78158
Type: Artigo de periódico
Title: THE MODULE OF DERIVATIONS OF A STANLEY-REISNER RING
Author: BRUMATTI, P
SIMIS, A
Abstract: An explicit description is given of the module Der(k[($) under bar X]/I, k[($) under bar X]/I) of the derivations of the residue ring k[($) under bar X]/I, where I is an ideal generated by monomials whose exponents are prime to the characteristic of the held k (this includes the case of square free monomials in any characteristic and the case of arbitrary monomials in characteristic zero). In the case where I is generated by square flee monomials, this description is interpreted in terms of the corresponding abstract simplicial complex Delta. Sharp bounds for the depth of this module are obtained in terms of the depths of the face rings of certain subcomplexes Delta(i) related to the stars of the vertices v(i) of A. The case of a Cohen-Macaulay simplicial complex Delta is discussed in some detail: it is shown that Der(k[Delta], k[Delta]) is a Cohen-Macaulay module if and only if depth Delta(i) greater than or equal to dim Delta - 1 for every vertex v(i). A measure of triviality of the complexes Delta(i) is introduced in terms of certain star corners of v(i). A curious corollary of the main structural result is an affirmative answer in the present context to the conjecture of Herzog-Vasconcelos on the finite projective dimension of the k[($) under bar X]/I-module Der(k[($) under bar X]/I, k[($) under bar X]/I).
Subject: DERIVATIONS
MONOMIALS
SIMPLICIAL COMPLEX
COHEN-MACAULAY
DEPTH
Editor: Amer Mathematical Soc
Rights: aberto
Identifier DOI: 10.2307/2161115
Date Issue: 1995
Appears in Collections:Unicamp - Artigos e Outros Documentos

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