Turkish Journal of Mathematics
DOI
-
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
First Page
363
Last Page
372
Recommended Citation
HASHEMI, EBRAHIM (2008) "Rickart-type Annihilator Conditions on Formal Power Series," Turkish Journal of Mathematics: Vol. 32: No. 4, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol32/iss4/1
