论文标题
$ \ Mathfrak {M}何时：\ Mathfrak {M} $几乎是Gorenstein戒指？
When is $\mathfrak{m}:\mathfrak{m}$ an almost Gorenstein ring?
论文作者
论文摘要
给定一维Cohen-Macaulay本地环$（R，\ Mathfrak {M}，K）$，我们证明当且仅当$ \ Mathfrak {M Mathfrak {M} $是ring $ \ Mathfrak {m} m}：\ Mathfrak {m Mathfrak {m Mathfrak {m} $的情况下，几乎是Gorenstein。然后，我们通过引入几乎规范的理想和gagl环的概念来概括这个结果，并证明$ r $是且仅当$ \ mathfrak {m} $是$ \ mathfrak {m mathfrak {m}的几乎规范理想时，才能证明$ r $是gagl。我们使用这个事实来表征$ \ mathfrak {m} {m}：\ mathfrak {m} $几乎是Gorenstein，但前提是$ r $具有最小的多重性。这是Chau，Goto，Kumashiro和Matsuoka证明的结果的概括，在$ \ Mathfrak {M}的情况下：\ Mathfrak {M Mathfrak {M} $是本地的，其残基字段与$ k $是同构的。
Given a one-dimensional Cohen-Macaulay local ring $(R,\mathfrak{m},k)$, we prove that it is almost Gorenstein if and only if $\mathfrak{m}$ is a canonical module of the ring $\mathfrak{m}:\mathfrak{m}$. Then, we generalize this result by introducing the notions of almost canonical ideal and gAGL ring and by proving that $R$ is gAGL if and only if $\mathfrak{m}$ is an almost canonical ideal of $\mathfrak{m}:\mathfrak{m}$. We use this fact to characterize when the ring $\mathfrak{m}:\mathfrak{m}$ is almost Gorenstein, provided that $R$ has minimal multiplicity. This is a generalization of a result proved by Chau, Goto, Kumashiro, and Matsuoka in the case in which $\mathfrak{m}:\mathfrak{m}$ is local and its residue field is isomorphic to $k$.
