SPECTRAL LOCALIZING SYSTEMS THAT ARE t-SPLITTING MULTIPLICATIVE SETS OF IDEALS

Title & Authors
SPECTRAL LOCALIZING SYSTEMS THAT ARE t-SPLITTING MULTIPLICATIVE SETS OF IDEALS
Chang, Gyu-Whan;

Abstract
Let D be an integral domain with quotient field K, A a nonempty set of height-one maximal t-ideals of D, F$\small{({\Lambda})={I{\subseteq}D|I}$ is an ideal of D such that $\small{I{\subseteq}P}$ for all $\small{P{\in}A}}$, and $\small{D_F({\Lambda})={x{\in}K|xA{\subseteq}D}$ for some $\small{A{\in}F({\Lambda})}}$. In this paper, we prove that if each $\small{P{\in}A}$ is the radical of a finite type v-ideal (resp., a principal ideal), then $\small{D_{F({\Lambda})}}$ is a weakly Krull domain (resp., generalized weakly factorial domain) if and only if the intersection $\small{D_{F({\Lambda})}={\cap}_{P{\in}A}D_P}$ has finite character, if and only if $\small{F({\Lambda})}$ is a t-splitting set of ideals, if and only if $\small{F({\Lambda})}$ is v-finite.
Keywords
spectral localizing system;t-splitting set of ideals;weakly Krull domain;generalized weakly factorial domain;
Language
English
Cited by
1.
POWER SERIES RINGS OVER PRÜFER v-MULTIPLICATION DOMAINS, Journal of the Korean Mathematical Society, 2016, 53, 2, 447
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