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KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS

김환구|오동렬|장규환
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회보 (Bulletin of the KMS)|제52권 제4호|pp. 1253-1268

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참고문헌

키워드

Kaplansky-type theoremupper to zeroprime (primary) elementgraded PvMDgraded GCD domaingraded G-GCD domaingraded B´ezout domaingraded valuation domaingraded Krull domaingraded π-domain
주제분류수학

초록

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, B´ezout domain, valuation domain, Krull domain, π-domain).

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, B´ezout domain, valuation domain, Krull domain, π-domain).

참고문헌 (23)

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관련 논문AI추천

GRADED INTEGRAL DOMAINS AND PRUFER-LIKE DOMAINS장규환대한수학회 · 대한수학회지2017 · 제54권 제6호Kaplansky-type Theorems, II김환구, 장규환경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제3호Graded integral domains in which each nonzero homogeneous ideal is divisorial장규환, Haleh Hamdi, Parviz Sahandi대한수학회 · 대한수학회보2019 · 제56권 제4호On t-almost Dedekind graded domains오동렬, 장규환대한수학회 · 대한수학회보2017 · 제54권 제6호ON GRADED KRULL OVERRINGS OF A GRADED NOETHERIAN DOMAIN박미희, 이은경대한수학회 · 대한수학회보2012 · 제49권 제1호ON ALMOST FACTORIALITY OF INTEGRAL DOMAINS임정욱장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제4호

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