On Mori domains and commutative rings with CC I

Research output: Contribution to journalArticlepeer-review


We prove here, among other results, that if A is a Mori domain containing an uncountable field, then any polynomial ring over A is Mori. The Mori property of a domain is determined by its maximal ideals. We use extensively a known characterization of Mori domains in terms of the chain condition on annihilators. We characterize Mori domains in terms of semivaluations and divisibility groups. We prove an analogue of Nagata's theorem for the Mori property and present an example of a completely integrally closed domain A, S a multiplicative subset of A generated by prime elements, such that A is completely integrally closed, but AS is not.

Original languageEnglish
Pages (from-to)247-268
Number of pages22
JournalJournal of Pure and Applied Algebra
Issue number3
StatePublished - 6 Feb 1989

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'On Mori domains and commutative rings with CC I'. Together they form a unique fingerprint.

Cite this