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• W2788156736 abstract "Let $ast $ be a finite character star operation defined on an integral domain $D.$ Call a nonzero $ast $-ideal $I$ of finite type a $ast $ -homogeneous ($ast $-homog) ideal, if $Isubsetneq D$ and $(J+K)^{ast }neq D$ for every pair $Dsupsetneq J,Ksupseteq I$ of proper $ast $ -ideals of finite type$.$ Call an integral domain $D$ a $ast $-Semi Homogeneous Domain ($ast $-SHD) if every proper principal ideal $xD$ of $D$ is expressible as a $ast $-product of finitely many $ast $-homog ideals. We show that a $ast $-SHD contains a family $mathcal{F}$ of prime ideals such that (a) $D=cap_{Pin mathcal{F}}D_{P},$ a locally finite intersection and (b) no two members of $mathcal{F}$ contain a common non zero prime ideal. The $ast $-SHDs include h-local domains, independent rings of Krull type, Krull domains, UFDs etc. We show also that we can modify the definition of the $ast $-homog ideals to get a theory of each special case of a $ast $-SH domain." @default.
• W2788156736 created "2018-03-06" @default.
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• W2788156736 date "2018-02-23" @default.
• W2788156736 modified "2023-09-27" @default.
• W2788156736 title "On $ast $-Semi Homogeneous Domains" @default.
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