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OVERRINGS OF t-COPRIMELY PACKED DOMAINS

김환구
대한수학회 (The Korean Mathematical Society)|2011.01|대한수학회지 (Journal of the KMS)|제48권 제1호|pp. 191-205

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참고문헌

키워드

t-coprimely packedt-compactly packedstrong Mori domainPrufer v-multiplication domaintQR-property(t-) flat
주제분류수학

초록

It is well known that for a Krull domain R, the divisor class group of R is a torsion group if and only if every subintersection of R is a ring of quotients. Thus a natural question is that under what conditions,for a non-Krull domain R, every (t-)subintersection (resp., t-linked overring) of R is a ring of quotients or every (t-)subintersection (resp.,t-linked overring) of R is at. To address this question, we introduce the notions of *-compact packedness and *-coprime packedness of (an ideal of) an integral domain R for a star operation * of nite character, mainly t or w. We also investigate the t-theoretic analogues of related results in the literature.

Abstract

It is well known that for a Krull domain R, the divisor class group of R is a torsion group if and only if every subintersection of R is a ring of quotients. Thus a natural question is that under what conditions,for a non-Krull domain R, every (t-)subintersection (resp., t-linked overring) of R is a ring of quotients or every (t-)subintersection (resp.,t-linked overring) of R is at. To address this question, we introduce the notions of *-compact packedness and *-coprime packedness of (an ideal of) an integral domain R for a star operation * of nite character, mainly t or w. We also investigate the t-theoretic analogues of related results in the literature.

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