For a property X of integral domains, D is said to be an MZ-X domain if DP has the property X for all associated prime ideals P of an integral domain D. Our first goal is to study some ring-theoret...

Integral domains issued from associated primes

In this paper we introduce two new generalizations of Krull domains: $\ast$-almost independent rings of Krull type ($\ast$-almost IRKTs) and $\ast$-almost generalized Krull domains ($\ast$-AGKDs), neither of which need be integrally closed. We characterize them using certain types of $\ast$-homogeneous ideals. To do this we introduce $\ast$-almost super-homogeneous ideals and $\ast$-almost super-SH domains. We prove that a domain $D$ is a $\ast$-almost IRKT if and only if $D$ is a $\ast$-almost super-SH domain and that a domain is a $\ast$-AGKD if and only if $D$ is a type 1 $\ast$-almost super-SH domain. Further, we study $\ast$-almost factorial general-SH domains ($\ast$-afg SH domains) and we prove that a domain $D$ is a $\ast$-afg-SH domain if and only if $D$ is a $\ast$-IRKT and an AGCD-domain.

Two generalizations of Krull domains

Abstract Call a t-ideal I of an integral domain R well-behaved if IRS is a t-ideal in RS for every multiplicatively closed subset S of R that is disjoint from I. We show that the set of well-behaved t-ideals has maximal elements and use the induced star operation to study the almost Krull domains (domains whose localizations are Krull) introduced by E. Pirtle.

Well-behaved prime t-ideals and almost Krull domains

Abstract In this paper, we construct some non-integrally closed domains in Gorenstein multiplicative ideal theory. For example, we show that there exists a Gorenstein Prüfer domain which is neither Gorenstein Dedekind nor Prüfer, and there exists a Gorenstein Krull domain which is neither Gorenstein Dedekind nor Krull. Also, we construct a non-integrally closed non-coherent domain in which all Gorenstein projective (resp., injective, flat) modules are projective (resp., injective, flat).

Some examples in Gorenstein multiplicative ideal theory

http://or.nsfc.gov.cn/bitstream/00001903-5/531718/1/1000014876495.pdf

Fanggui Wang

Papers

A half-centered star-operation on an integral domain