FT-domains and Gorenstein Prüfer v-multiplication domains

Abstract

It was shown by Kang (1989) that a domain R is a Krull domain if and only if R is a Mori domain and a PvMD. In this paper, we extend this result to Gorenstein multiplicative ideal theory. To do this, we introduce the concepts of FT-domains and G-PvMDs, and study them by a new star-operation, i.e., the f-operation. We prove that (1) a domain R is an integrally closed FT-domain if and only if R is a P-domain; (2) a domain R is a G-PvMD if and only if R is a g-coherent FT-domain; (3) a domain R is a G-Krull domain if and only if R is a Mori domain and a G-Pv$v$MD.