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 …

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 $ R $ be a ring and $\mathscr {C} $ be a class of some finitely presented left $ R $-
modules. A left $ R $-module $ M $ is called $\mathscr {C} $-injective if Ext $^ 1_R (C, M) …

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, let I be an ideal of R, and let n be a fixed positive integer. We define and
study In-injective modules and In-flat modules. Moreover, we define and study left In …

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 …

Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case
every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n …

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. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

A ring R is said to be left n-semihereditary, if every n-generated left ideal of R is projective. It
is shown that for a ring R, the following statements are equivalent:(1) R is left n …