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- W1986407463 abstract "Abstract Let ℜ be the class of commutative rings R with comparable regular elements, that is, given two non zero-divisors in R , one divides the other. Applying the notion of V -valuation due to Harrison and Vitulli, we define the class V -val of V -valuated rings, which is contained in ℜ and contains the class of Manis valuation rings. We prove that these inclusions of classes are both proper. We investigate Prüfer rings inside ℜ , showing that there exist Prüfer rings which lie in ℜ but not in V -val; we prove that a ring R is a Prüfer valuation ring if and only if it is Prüfer and V -valuated, if and only if its lattice of regular ideals is a chain. Finally, we introduce and investigate the ideal I ∞ of a ring R ∈ ℜ , which corresponds to the counterimage of ∞, whenever R is V -valuated." @default.
- W1986407463 created "2016-06-24" @default.
- W1986407463 creator A5071863360 @default.
- W1986407463 date "1996-02-01" @default.
- W1986407463 modified "2023-09-26" @default.
- W1986407463 title "Commutative rings with comparable regular elements" @default.
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- W1986407463 doi "https://doi.org/10.1017/s144678870003740x" @default.
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