Generalized Gorenstein Arf rings

Abstract

In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain new characterizations and examples of Arf rings, and give applications of our argument to numerical semigroup rings and certain idealizations. In particular, we generalize a beautiful result of Barucci and Fröberg concerning Arf numerical semigroup rings.

arXiv comment15 pages

References in corpus (6)

• 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
• Topics on $2$-almost Gorenstein rings
• Characterization of generalized Gorenstein rings
• When is $R⋉I$ an almost Gorenstein local ring?

Cited by in corpus (4)

• Almost Gorenstein rings arising from fiber products
• Construction of strictly closed rings
• Decomposition of integrally closed ideals in Arf rings
• Reflexive modules, self-dual modules and Arf rings