Slightly (m, n)-coherent rings and (m, n)-homological dimensions. Issue 11 (1st November 2020) - Zhao, Renyu
Abstract: Let R be a ring and m, n two fixed positive integers. In this article, R is defined to be left slightly ( m, n )-coherent if each n -generated submodule of the left R -module R m is ( m, n )-projective. It is shown that R is left slightly ( m, n )-coherent if and only if the cotorsion pair ( P m, n, I m, n ) is hereditary if and only if R is left ( m, n )-coherent and the cotorsion pair ( F m, n, C m, n ) is hereditary, where P m, n (resp., I m, n ) stands for the class of all ( m, n )-projective (resp., ( m, n )-injective) left R -modules, and F m, n (resp., C m, n ) denotes the classes of all ( m, n )-flat (resp., ( m, n )-cotorsion) right R -modules. As applications, ( m, n )-homological dimensions of modules and rings over slightly ( m, n )-coherent rings are studied.