Rickart-type Annihilator Conditions on Formal Power Series

Authors: EBRAHIM HASHEMI

Abstract: Let R be an \alpha-rigid ring and R_0[[x;\alpha]] 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 R_0[[x;\alpha]]\in R_{r1} if and only if R_0[[x;\alpha]]\in R_{\ell 1} if and only if R_0[[x;\alpha]]\in qR_{r2}. An example to show that, \alpha-rigid condition on R is not superfluous, is provided.

Keywords: Annihilator conditions; Nearrings; Skew power series; Baer rings; \alpha-rigid rings; Rickart rings

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