Almost Gorenstein rings
Almost Gorenstein rings
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DOI：
10.1016/j.jalgebra.2013.01.025
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
S. Goto;Naoyuki Matsuoka;T. Phuong
中科院分区：
文献类型：
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作者：
S. Goto;Naoyuki Matsuoka;T. Phuong
Barucci和Fröberg(1997)[2]在解析非分支局部环（R,m）的情况下引入了几乎Gorenstein环的概念。在这项工作中，我们提供了一个框架，使我们能够将这一概念推广到包括分析分支情况。因此，对于任何1维的Cohen-Macaulay局部环（R,m），我们完全一般地解决了确定自同态代数m:m何时为Gorenstein的问题。我们还根据理想化原理提供了环几乎是格伦斯坦的特征。本文还探讨了几个例子。
Barucci and Fröberg (1997) [2] introduced the notion of an almost Gorenstein ring in the case of an analytically unramified local ring (R,m). In this work we provide a framework that allows us to generalize this notion to include the analytically ramified case. As a consequence, for any Cohen–Macaulay local ring (R,m) of dimension one we solve in full generality the problem of determining when the endomorphism algebra m:m is Gorenstein. We also provide characterizations for rings to be almost Gorenstein in connection with the principle of idealization. Several examples are explored as well.