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http://dx.doi.org/10.4134/JKMS.j210180

ON 𝜙-EXACT SEQUENCES AND 𝜙-PROJECTIVE MODULES  

Zhao, Wei (Department of Mathematics Nanjing University and School of Mathematics ABa Teachers University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1513-1528 More about this Journal
Abstract
Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → RNil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → MNil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.
Keywords
${\phi}$-exact sequence; nonnil-divisible module; ${\phi}$-projective module;
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