This paper deals with local rings R possessing an m-canonical ideal ω, R ⊆ ω. In particular those rings such that the length lR (ω / R) is as short as possible are studied. The same notion for one-dimensional local Cohen-Macaulay rings was introduced and studied with the name of Almost Gorenstein. Some necessary conditions, that become also sufficient under additional hypotheses, are given and examples are provided also in the non-Noetherian case. The case when the maximal ideal of R is stable is also studied. © 2008 Elsevier B.V. All rights reserved.
Local rings of minimal length / Barucci, Valentina. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 213:6(2009), pp. 991-996. [10.1016/j.jpaa.2008.11.007]
Local rings of minimal length
BARUCCI, Valentina
2009
Abstract
This paper deals with local rings R possessing an m-canonical ideal ω, R ⊆ ω. In particular those rings such that the length lR (ω / R) is as short as possible are studied. The same notion for one-dimensional local Cohen-Macaulay rings was introduced and studied with the name of Almost Gorenstein. Some necessary conditions, that become also sufficient under additional hypotheses, are given and examples are provided also in the non-Noetherian case. The case when the maximal ideal of R is stable is also studied. © 2008 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
