abstract_textpLet R be a domain with its field Q of quotients, M an R-module and n a fixed non-negative integer. Then M is called n-Matlis cotorsion if Ext(R)(k)(Q, M) = 0 for any integer k n. Also M is said to be n-Matlis flat if Ext(R)(1)(M, N) = 0 for any n-Matlis cotorsion R-module N. We proved that (MFn, MCn) is a complete hereditary cotorsion theory, where MFn (respectively, MCn) denotes the class of all n-Matlis flat (respectively, n-Matlis cotorsion) R-modules. In this paper, it is proved that R is an n-Matlis domain if and only if epic images of (n- 1)-Matlis cotorsion R-modules are again (n- 1)-Matlis cotorsion if and only if (n - 1)-Matlis flat R-modules are of projective dimension = 1 if and only if MC0.gl.dim(R) = n if and only if MCn.gldim(R) = 0./p/abstract_text
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