Almost Gorenstein rings

作者：Goto Shiro; Matsuoka Naoyuki^*; Tran Thi Phuong

来源：Journal of Algebra, 2013, 379: 355-381.

DOI：10.1016/j.jalgebra.2013.01.025

• Cohen-Macaulay local ring
• Gorenstein ring
• Almost Gorenstein ring
• Hilbert coefficient
• Canonical ideal

Barucci and Froberg (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 in : in 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.

• 出版日期2013-4-1