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ON ϕ-PSEUDO ALMOST VALUATION RINGS
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 Title & Authors
ON ϕ-PSEUDO ALMOST VALUATION RINGS
Esmaeelnezhad, Afsaneh; Sahandi, Parviz;
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 Abstract
The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be -ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a -ring R is said to be a -pseudo-strongly prime ideal if, whenever and , then there exists an integer such that either or . If each prime ideal of R is a -pseudo strongly prime ideal, then we say that R is a -pseudo-almost valuation ring (-PAVR). Among the properties of -PAVRs, we show that a quasilocal -ring R with regular maximal ideal M is a -PAVR if and only if V
 Keywords
-ring;valuation domain;pseudo-valuation ring;almost valuation ring;-PAVR;chained ring;
 Language
English
 Cited by
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