Título inglés | On the free character of the first Koszul homology module. |
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Título español | Sobre el carácter libre del primer módulo de homología de Koszul. |
Autor/es | García Rodicio, Antonio |
Organización | Dep. Alg. Fac. Mat. Univ. Santiago de Compostela, Santiago de Compostela (La Coruña), España |
Revista | 0213-8743 |
Publicación | 1991, 6 (2-3): 126-128, 5 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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. |
Clasificación UNESCO | 120105 ; 120107 |
Palabras clave español | Algebras conmutativas ; Métodos homológicos ; Anillo local Noetheriano |
Código MathReviews | MR1185357 |
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