Almost Gorenstein rings
Commutative Algebra
2011-06-09 v2
Abstract
The notion of almost Gorenstein ring given by Barucci and Fr{\"o}berg \cite{BF} in the case where the local rings are analytically unramified is generalized, so that it works well also in the case where the rings are analytically ramified. As a sequel, the problem of when the endomorphism algebra of is a Gorenstein ring is solved in full generality, where denotes the maximal ideal in a given Cohen-Macaulay local ring of dimension one. Characterizations of almost Gorenstein rings are given in connection with the principle of idealization. Examples are explored.
Cite
@article{arxiv.1106.1301,
title = {Almost Gorenstein rings},
author = {Shiro Goto and Naoyuki Matsuoka and Tran Thi Phuong},
journal= {arXiv preprint arXiv:1106.1301},
year = {2011}
}