ALMOST F-INJECTIVE MODULES AND ALMOST FLAT MODULES

Year 2014, Volume: 16 Issue: 16, 115 - 126, 01.12.2014

Zhu Zhanmin

https://doi.org/10.24330/ieja.266231

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