Let $ R $ be a ring, $ n $ be an non-negative integer and $ d $ be a positive integer or $\infty
$. A right $ R $-module $ M $ is called\emph {$(n, d)^* $-projective} if ${\rm Ext}^ 1_R (M …

Let R be a ring, and let n, d be non-negative integers. A right R-module M is called (n, d)-
projective if Ext d+ 1 R (M, A)= 0 for every n-copresented right R-module A. R is called right 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 …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

Let T be a weak torsion class of left R-modules and na positive integer. A left R-module M is
called (T, n)-injective if Ext R n (C, M)= 0 for each (T, n+ 1)-presented left R-module C; a right …

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. 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 …

Recall that a ring R is said to be left coherent [2, 7] if every finitely generated left ideal of R is
finitely presented, a ring R is said to be left semihereditary if every finitely generated left …

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 m and n be fixed positive integers. R is called a right (m, n)-injective ring if every right R-
homomorphism from an n-generated submodule of the right R-module R m to R extends to …