On Two-Sided Right Ideals in Chain Domains.
The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.
We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
In this note, for a ring endomorphism and an -derivation of a ring , the notion of weakened -skew Armendariz rings is introduced as a generalization of -rigid rings and weak Armendariz rings. It is proved that is a weakened -skew Armendariz ring if and only if is weakened -skew Armendariz if and only if is weakened -skew Armendariz ring for any positive integer .
The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module , there exists a module such that is weakly injective in , for any . Similarly, if is projective and right perfect in , then there exists a module such that is weakly projective in , for any . Consequently, over a right perfect ring every module is a direct summand of a weakly projective module. For...
We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.