Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if
every n-generated submodule of M is finitely presented (resp. projective). We investigate the …

Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of
S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator ann M n …

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 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 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 …

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 …

According to Bourbaki [1, pp. 62–63, Exercise 11], a left (resp. right) A-module M is said to
be pseudo-coherent if every finitely generated submodule of M is finitely presented, and is …

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 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) …

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 …