Research articles

On ($\sigma$-$\delta$)-rings over Noetherian rings

Vijay Kumar Bhat^a, Meeru Abrol^a, Latif Hanna^b, Maryam Alkandari<sup>b

a</sup> Department of Mathematics, SMVD University, Katra, India-182320
^b Department of Mathematics, Kuwait University, Kuwait

Аннотация: For a ring $R$, an endomorphism $\sigma$ of $R$ and a $\sigma$-derivation $\delta$ of $R$, we introduce ($\sigma$-$\delta$)-ring and ($\sigma$-$\delta$)-rigid ring which are the generalizations of $\sigma(*)$-rings and $\delta$-rings, and investigate their properties. Moreover, we prove that a ($\sigma$-$\delta$)-ring is $2$-primal and its prime radical is completely semiprime.

Ключевые слова и фразы: endomorphism, derivation, $\sigma(*)$-rings, $\delta$-ring, $2$-primal ring, ($\sigma$-$\delta$)-ring, ($\sigma$-$\delta$)-rigid ring.

MSC: 16N40, 16P40, 16W20

Поступила в редакцию: 12.01.2015

Язык публикации: английский