Rickart-type Annihilator Conditions on Formal Power Series

Authors : Ebrahim Hashemi

Pages : 363-372

View : 15 | Download : 9

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Let R be an a-rigid ring and R0[[x;a]] be the nearring of a formal skew power series in which addition and substitution are used as operations. It is shown that R is Rickart and any countable family of idempotents of R has a join in I(R) if and only if R0[[x;a]]\in Rr1 if and only if R0[[x;a]]\in R\ell 1 if and only if R0[[x;a]]\in qRr2. An example to show that, a-rigid condition on R is not superfluous, is provided.
Keywords : Annihilator conditions, Nearrings, Skew power series, Baer rings, a-rigid rings, Rickart rings