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 …

Let R be a ring, n, d be fixed non-negative integers, the class of (n, d)-injective left R-
modules, and the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left …

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-
injective if Ext d+ 1 R (P, M)= 0 for any n-presented R-module P. M is said to be (n, d) …

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 ring and n be a positive integer. R is called left n-coherent, if every n-presented
left R-module is (n+ 1)(n+ 1)-presented. A left R-module M is called (n, 0)-injective if Ext …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

Let R be a ring, na fixed non-negative integer and ℱℐ n (ℱ n) the class of all left (right) R-
modules of FP-injective (flat) dimension at most n. A left R-module M (resp., right R-module …

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,
n)-injective if for any (m, n)-presented right R-module P; M is called (m, n)-flat if for any (m, n) …

Let $ R $ be a ring and $ n $ a fixed positive integer. A right $ R $-module $ M $ is called
strongly $ J $-$ n $-injective if every $ R $-homomorphism from an $ n $-generated small …

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 …