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arXiv · 1912.02306

Two generalizations of Krull domains

Shiqi Xing·Daniel D. Anderson·Muhammad Zafrullah
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Abstract

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.

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Shiqi Xing, Daniel D. Anderson, Muhammad Zafrullah. 2019-12-04. Two generalizations of Krull domains. https://arxiv.org/abs/1912.02306

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