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w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS
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 Title & Authors
w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS
Wang, Fanggui; Kim, Hwankoo;
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 Abstract
Let R be a commutative ring with identity. An R-module M is said to be w-projective if (M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Prfer v-multiplication domain.
 Keywords
w-projective module;w-flat module;w-injective module;finite type;w-semi-hereditary ring;
 Language
English
 Cited by
1.
THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS, Bulletin of the Korean Mathematical Society, 2015, 52, 4, 1327  crossref(new windwow)
2.
w-LinkedQ0-Overrings andQ0-Prüferv-Multiplication Rings, Communications in Algebra, 2016, 44, 9, 4026  crossref(new windwow)
3.
Overrings of Prüfer v-multiplication domains, Journal of Algebra and Its Applications, 2016, 1750147  crossref(new windwow)
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