A note on Matlis localizations

Abstract

Let R be a commutative ring and S a multiplicative subset of R. A ring R is called an S-Matlis ring if ${\text{pd}}_R{R}_S\le 1$. In this note, we give some new characterizations of S-Matlis rings in terms of S-strongly flat modules, S-weakly cotorsion modules and S-h-divisible modules.

Keywords:

• S-h-divisible module
• S-Matlis ring
• S-strongly flat module
• S-weakly cotorsion module

2020 Mathematics Subject Classification:

• Primary: 13C11
• Secondary: 13C13