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KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS
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 Title & Authors
KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS
CHANG, GYU WHAN; KIM, HWANKOO; OH, DONG YEOL;
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 Abstract
It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky's theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, domain, valuation domain, Krull domain, -domain).
 Keywords
Kaplansky-type theorem;upper to zero;prime (primary) element;graded PvMD;graded GCD domain;graded G-GCD domain;graded domain;graded valuation domain;graded Krull domain;graded -domain;
 Language
English
 Cited by
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