Dergiler / Turkish Journal of Mathematics / 2008 / Cilt: 32 - Sayı: 4
Rickart-type Annihilator Conditions on Formal Power Series
- Sayfa
- 363–372
- DOI
- —
Özet
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.
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.