Shinya Kumashiro

Characterization of almost Gorenstein rings in terms of the trace ideal

We provide a characterization of one-dimensional almost Gorenstein rings in terms of the trace ideal. As an application, we investigate the almost Gorenstein property of certain ℤ 2 -graded rings.

Quasi‐Factorially Closed Subalgebras of Laurent Polynomial Rings

ABSTRACT Let be a domain and the Laurent polynomial ring over . In this paper we study pre‐factorially closed (pfc) and quasi‐factorially closed (qfc) ‐subalgebras of , which generalize the notion of factorially closed subalgebras. We first establish a localization criterion for...