Almost Gorenstein rings

By S. Goto, Naoyuki Matsuoka, T. Phuong. 2011

117 citations recorded by the source corpus.

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 $\m : \m$ of $\m$ is a Gorenstein ring is solved in full generality, where $\m$ 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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1a8613c41b1d5ffae3579ff5ea3cd2b7a524c036

How researchers see this paper

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In Algebra and Number Theory

1. S. Goto
2. Ryo Takahashi
3. D. White

In Geometry and Topology

1. S. Goto
2. Ryo Takahashi
3. D. White
4. Hailong Dao
5. Greg Stevenson

Citations in the corpus

• Almost Gorenstein rings – towards a theory of higher dimension (2014, background): “Conversely, assume that R is an almost Gorenstein local ring in the sense of [14] and that R/m is infinite.”