In this article, several characterizations of certain classes of rings via FC-purity and I-purity
are considered. Among others results, it is shown that every I-pure injective left R-module is …

ON N-COHERENT RINGS, N-HEREDITARY RINGS AND N-REGULAR RINGS Page 1 Archive
of SID Bulletin of the Iranian Mathematical Society Vol. 37 No. 4 (2011), pp 251-267. ON …

Let R be a commutative ring, and let C be a semidualizing R-module. We introduce the
notion of finitely presented C-injective modules, finitely presented C-flat modules, weak C …

Let $ n, d $ be two non-negative integers. A left $ R $-module $ M $ is called $(n, d) $-
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

Let R and S be rings and RCS a semidualizing bimodule. We show that the supremum of the
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …

In this paper, by taking the class of all C 3 (or D 3) right R-modules for general envelopes
and covers, we characterize a semisimple artinian ring (or a right perfect ring) via D 3-covers …

Let $ R $ be a commutative ring with an identity, and $ S $ a multiplicative subset of $ R $. In
this paper, we introduce the notion of $ S $-injective modules as a weak version of injective …

In this note, we consider certain generalizations of injectivity and p-injectivity in connection
with von Neumann regular rings, self-injective regular rings, II-regular rings, semi-simple …