On the free character of the first Koszul homology module.

García Rodicio, Antonio. "On the free character of the first Koszul homology module.." Extracta Mathematicae 6.2-3 (1991): 126-128. <http://eudml.org/doc/39932>.

@article{GarcíaRodicio1991,
abstract = {Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1(E) is a free A/I-module.- (André [2]): Assume that A is a complete intersection. Then, A/I is complete intersection if and only if H1(E)2 = H2(E) and H1(E) is a free module.The purpose of this note is to generalize both results.},
author = {García Rodicio, Antonio},
journal = {Extracta Mathematicae},
keywords = {Algebras conmutativas; Métodos homológicos; Anillo local Noetheriano; Koszul homology module; Jacobi-Zariski sequences; complete intersection; local noetherian ring; Koszul complex},
language = {eng},
number = {2-3},
pages = {126-128},
title = {On the free character of the first Koszul homology module.},
url = {http://eudml.org/doc/39932},
volume = {6},
year = {1991},
}

TY - JOUR
AU - García Rodicio, Antonio
TI - On the free character of the first Koszul homology module.
JO - Extracta Mathematicae
PY - 1991
VL - 6
IS - 2-3
SP - 126
EP - 128
AB - Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1(E) is a free A/I-module.- (André [2]): Assume that A is a complete intersection. Then, A/I is complete intersection if and only if H1(E)2 = H2(E) and H1(E) is a free module.The purpose of this note is to generalize both results.
LA - eng
KW - Algebras conmutativas; Métodos homológicos; Anillo local Noetheriano; Koszul homology module; Jacobi-Zariski sequences; complete intersection; local noetherian ring; Koszul complex
UR - http://eudml.org/doc/39932
ER -