ALMOST F-INJECTIVE MODULES AND ALMOST FLAT MODULES

Authors : Zhu Zhanmin

Pages : 115-126

Doi:10.24330/ieja.266231

View : 12 | Download : 11

Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :A left R-module M is called almost F-injective, if every R-homomorphism from a finitely presented left ideal to M extends to a homomorphism of R to M. A right R-module V is said to be almost flat, if for every finitely presented left ideal I, the canonical map V ⊗ I → V ⊗R is monic. A ring R is called left almost semihereditary, if every finitely presented left ideal of R is projective. A ring R is said to be left almost regular, if every finitely presented left ideal of R is a direct summand of RR. We observe some characterizations and properties of almost F-injective modules and almost flat modules. Using the concepts of almost F-injectivity and almost flatness of modules, we present some characterizations of left coherent rings, left almost semihereditary rings, and left almost regular rings.
Keywords : Almost F injective modules, almost flat modules, coherent rings, almost semihereditary rings, almost regular rings