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 P$v$MD. In this paper, we extend this result to Gorenstein multiplicative ideal theory. To do this, we introduce the concepts of $FT$-domains and G-P$v$MDs, 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-P$v$MD 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-P$v$$v$MD.