J. Korean Math. Soc. 2007; 44(6): 1267-1279
Printed November 1, 2007
Copyright © The Korean Mathematical Society.
Ebrahim Hashemi
Shahrood University of Thechnology
For a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$ of a ring $R$, we study relation between the set of annihilators in $R$ and the set of annihilators in nearring $R[x;\alpha,\delta]$ and $R_0[[x;\alpha]]$. Also we extend results of Armendariz on the Baer and p.p. conditions in a polynomial ring to certain analogous annihilator conditions in a nearring of skew polynomials. These results are somewhat surprising since, in contrast to the skew polynomial ring and skew power series case, the nearring of skew polynomials and skew power series have substitution for its "multiplication" operation.
Keywords: annihilator conditions, nearrings, skew power series, skew polynomial rings, Baer ring, quasi-Baer rings, $\alpha$-rigid rings, Rickart rings.
MSC numbers: 16Y30, 16S36
2019; 56(2): 539-558
2005; 42(2): 353-363
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd