On τ-centralizers of semiprime rings

Let R be a semiprime 2-torsion free ring, and let τ be an endomorphism of R. Under some conditions we prove that a left Jordan τ-centralizer of R is a left τ-centralizer of R. Under the same conditions we also prove that a Jordan τ-centralizer of R is a τ-centralizer of R. We thus generalize Zalar’s results to the case of τ-centralizers of R.     

On directional derivatives of semiprime rings

Dedicated to the 70th birthday of Anatolii Illarionovich Shirshov.     

On regular semigroup rings

Communicated by L. N. Shevrin     

On when small semiprime rings are slender

Various semiprime rings with less than 2^w elements are shown to be slender     

Distributive semiprime rings

It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx ⁿ A=Ax ⁿ . We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings. Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 736–761, November, 1995.     

On the derivations of semigroup rings

In questo lavoro studiamo i generatori del modulo delle derivazioni di anelli di semigruppoR=k[S], dandone una caratterizzazione sotto opportune ipotesi suS.