Topics on $2$-almost Gorenstein rings

Abstract

The notion of $2$-almost Gorenstein ring is a generalization of the notion of almost Gorenstein ring in terms of Sally modules of canonical ideals. In this paper, we deal with two different topics related to $2$-almost Gorenstein rings. The purposes are to determine all the Ulrich ideals in $2$-almost Gorenstein rings and to clarify the structure of minimal free resolutions of $2$-almost Gorenstein rings.

12 pages

References in corpus (4)

• On the almost Gorenstein property in Rees algebras of contracted ideals
• Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals
• Invariants of Cohen-Macaulay rings associated to their canonical ideals
• On the almost Gorenstein property of determinantal rings

Cited by in corpus (2)

• Generalized Gorenstein Arf rings
• Characterization of generalized Gorenstein rings