Pseudo-almost valuation rings

Document Type: Research Paper

Authors

Department of‎ ‎Mathematics‎, ‎University‎ ‎of Kashan‎, ‎P.O‎. ‎Box 8731751167‎, ‎Kashan‎, ‎Iran

Abstract

The aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎It is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordered prime ideals‎.

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