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On uniformly strongly prime Γ-semirings (II)

Tapan Kumar Dutta, Suhrid Dhara (2006)

Discussiones Mathematicae - General Algebra and Applications

The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.

On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav Mittal, Rajendra Kumar Sharma (2021)

Mathematica Bohemica

We characterize the unit group of semisimple group algebras 𝔽 q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ( ( C 3 × C 3 ) C 3 ) C 2 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.

On valuations of nearfields

Dalibor Klucký, Libuše Marková (1983)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On weakened ( α , δ ) -skew Armendariz rings

Alireza Majdabadi Farahani, Mohammad Maghasedi, Farideh Heydari, Hamidagha Tavallaee (2022)

Mathematica Bohemica

In this note, for a ring endomorphism α and an α -derivation δ of a ring R , the notion of weakened ( α , δ ) -skew Armendariz rings is introduced as a generalization of α -rigid rings and weak Armendariz rings. It is proved that R is a weakened ( α , δ ) -skew Armendariz ring if and only if T n ( R ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz if and only if R [ x ] / ( x n ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz ring for any positive integer n .

On weakly projective and weakly injective modules

Mohammad Saleh (2004)

Commentationes Mathematicae Universitatis Carolinae

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 M , there exists a module K σ [ M ] such that K N is weakly injective in σ [ M ] , for any N σ [ M ] . Similarly, if M is projective and right perfect in σ [ M ] , then there exists a module K σ [ M ] such that K N is weakly projective in σ [ M ] , for any N σ [ M ] . Consequently, over a right perfect ring every module is a direct summand of a weakly projective module. For...

On wings of the Auslander-Reiten quivers of selfinjective algebras

Marta Kwiecień, Andrzej Skowroński (2005)

Colloquium Mathematicae

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.

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