Journal of the
Korean Mathematical Society JKMS

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