σ∗-projective covers and σ-Artinian rings

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

ON Σ-q RINGS

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

On Σ-v Rings

We discuss various properties of a ring over which each simple module is Σ-injective. We shall consider associative rings with identity. Our modules will be unital right modules unless stated otherwise. The class of right V rings was introduced by Villamayor [20]. A ring R is called a right V ring if each simple right Rmodule is injective. It is a well-known unpublished result due to Kaplansky ...

Ore Extensions over Weak Σ - Rigid Rings

Let R be a ring, σ an automorphism of R and δ a σ-derivation of R. We recall that a ring R is said to be a δ-ring if aδ(a) ∈ P (R) implies a ∈ P (R), where P (R) denotes the prime radical of R. It is known that, if R is a Noetherian ring, σ an automorphism of R such that aσ(a) ∈ P (R) implies a ∈ P (R) and δ a σ-derivation of R such that R is a δ-ring with σ(δ(a)) = δ(σ(a)), for all a ∈ R, then...

σ-Normality of Topological Spaces