# On the free character of the first Koszul homology module.

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 126-128
- ISSN: 0213-8743

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topGarcía 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 -

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