In this paper, we introduce Matlis flat modules as a generalization of copure flat modules and give their characterizations. We prove that if R is a commutative Artinian ring and S ⊂ R is a multiplicative set, then S^-1M is a Matlis flat S^-1R-module for any Matlis flat R-module M. Also we prove that every module has Matlis flat preenvelope over commutative Artinian rings.

Tbilisi Mathematical Journal, Vol. 9(2) (2016), pp. 105-114