Ebrahim HASHEMI

Rickart-type Annihilator Conditions on Formal Power Series

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.

Anahtar Kelimeler:

Annihilator conditions; Nearrings; Skew power series; Baer rings; a-rigid rings; Rickart rings

Rickart-type Annihilator Conditions on Formal Power Series

Keywords:

Annihilator conditions; Nearrings; Skew power series; Baer rings; a-rigid rings; Rickart rings,

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Department of Mathematics, Shahrood University of Thechnology, Shahrood-IRAN e-mail: eb hashemi@shahroodut.ac.ir e-mail: eb hashemi@yahoo.com