Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …

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 Ext1 (P, M)= 0 for any (m, n)-presented right R-module P; M is said to be (m, n) …

Let $\cal F $ be a left Gabriel topology on a ring $ R $ and $\cal X $ be a special class of left
$ R $-modules (for example, the class of all quasi-continuous left $ R $-modules in $\sigma …

An R-module M is said to be bounded if for any essential sub-module N of M, there exists an
ideal K of R with K/ann (M) essential as a right ideal in R/ann (M) such that MK⊆ N, The …

Let R be a commutative ring with a nonzero identity and M an R-module. Set ϕ-tor (M)={x∈
M| sx= 0 for some s∈ R∖ Nil (R)}, if ϕ-tor (M)= M then M is called a ϕ-torsion module. An R …

Let us first recall some definitions from [3]. A ring R is said to be a left-n-FGFP ring (right-n-
FGFP ring) if any n-generated flat left (right) R-module is projective. R is called an n-FGFP …

Let R be any ring with identity, and let M be a unitary left R-module. A submodule K of M is
called generalized coessential submodule of N in M, if (N)/K⊆[Rad] _g (M/K). A module M is …

Let us first recall some definitions from [3]. A ring R is said to be a left-n-FGFP ring (right-n-
FGFP ring) if any τι-generated flat left (right) ii-module is projective. R is called an n-FGFP …

A ring R is called a right WPF-ring (weak PF-ring) if R is a semiperfect right simple-injective
ring with essential right socle. The class of right WPF-rings is broader than that of right PF …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …