Slightly (m, n)-coherent rings and (m, n)-homological dimensions. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Zhao, Renyu; Li, Ruilin
• Is Part Of: Communications in algebra. Volume 48:Issue 11(2020)
• Page Start: 4809
• Page End: 4823
• Publication Date: 2020-11-01
• Subjects: Slightly (m, n)-coherent ring; (m, n)-injective module; (m, n)-projective module; (m, n)-flat module; (m, n)-homological dimension; 16D40 -- 16D50 -- 16P70; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1771352
• Languages: English
• ISSNs: 0092-7872

Abstract

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.