Pseudo-almost valuation rings
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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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pseudo-almost valuation rings
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 ordere...
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Recall that a commutative ring R is said to be a pseudo-valuation ring if every prime ideal of R is strongly prime. We define a completely pseudovaluation ring. Let R be a ring (not necessarily commutative). We say that R is a completely pseudo-valuation ring if every prime ideal of R is completely prime. With this we prove that if R is a commutative Noetherian ring, which is also an algebra ov...
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Journal title
volume 41 issue 4
pages 815- 824
publication date 2015-08-01
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