This paper introduces and studies homological properties of new classes of modules,
namely, the $\mathcal F_1 $-flat modules and the $\mathcal F_1^{\fp} $-flat modules, where …

For a fixed given right R-module M, so-called M-flat left R-modules are investigated, which
are flat relative to short exact sequences in the subcategory σ [M] subgenerated by M. The …

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 be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

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 …

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 …

We study, in this article, the FGT-injective dimensions of Π-coherent rings. If R is right Π-
coherent, and TI (resp. TF) stands for the class of FGT-injective (resp. FGT-flat) R-modules …

Recall that a left module A (resp. right module B) is said to be singly injective (resp. singly
flat) if Ext^ 1 _ R (F/K, A)= 0 E xt R 1 (F/K, A)= 0 (resp. Tor _ 1^ R (B, F/K)= 0 Tor 1 R (B, F/K) …

A ring is called n-Perfect (n≥ 0) if every flat module has projective dimension less or equal
than n. In this paper we introduce “Strong n-Perfect rings” which is in some way a …

In this paper, we introduce and study the concepts of weak n-injective and weak n-flat
modules in terms of super finitely presented modules whose projective dimension is at most …