Some notes on $GQN$ rings

Abstract

A ring R is called a generalized quasinormal ring (abbreviated as GQN ring) if ea ∈ N (R) for each e ∈ E(R) and a ∈ N (R) . The class of GQN rings is a proper generalization of quasinormal rings and N I rings. Many properties of quasinormal rings are extended to GQN rings. For a GQN ring R and a ∈ R , it is shown that: 1) if a is a regular element, then a is a strongly regular element; 2) if a is an exchange element, then a is clean; 3) if R is a semiperiodic ring with J(R) ̸ = N (R) , then R is commutative; 4) if R is an M V N R , then R is strongly regular.

Generalized weakly central reduced rings

“…, and so R is not a left M C2 ring. By [20,Example 2.11], every simple singular left R−module is injective. Clearly,…”