A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

POOR MODULES: THE OPPOSITE OF INJECTIVITY Page 1 Glasgow Math. J. 52A (2010) 7–17.
C Glasgow Mathematical Journal Trust 2010. doi:10.1017/S001708951000025X. POOR …

A ring R is called right weakly continuous if the right annihilator of each element is essential
in a summand of R, and R satisfies the right C2-condition (every right ideal that is isomorphic …

An R-module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with
M= A 1⊕ A 2 and f: A 1→ A 2 is an R-homomorphism with ker f⊆⊕ A 1, we have I mf⊆⊕ A …

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring
is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or …

A ring R is called a right Ikeda-Nakayama ring (right IN-ring) if the left annihilator of the
intersection of any two right ideals is the sum of the two left annihilators. In this paper we …

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-
homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple …

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

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

It is proved that if every cyclic right R-module is torsionless and R is a left CS-ring then R is
semiperfect left continuous with soc (RR) essential in RR. As a consequence every right …