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http://dx.doi.org/10.4134/JKMS.2014.51.3.509

w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS  

Wang, Fanggui (College of Mathematics Sichuan Normal University)
Kim, Hwankoo (School of Computer and Information Engineering Hoseo University)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.3, 2014 , pp. 509-525 More about this Journal
Abstract
Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(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 $R_m$ 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 Pr$\ddot{u}$fer v-multiplication domain.
Keywords
w-projective module; w-flat module; w-injective module; finite type; w-semi-hereditary ring;
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Times Cited By KSCI : 1  (Citation Analysis)
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