ON ANNIHILATOR IDEALS OF A NEARRING OF SKEW POLYNOMIALS OVER A RING

Title & Authors
ON ANNIHILATOR IDEALS OF A NEARRING OF SKEW POLYNOMIALS OVER A RING
Hashemi, Ebrahim;

Abstract
For a ring endomorphism $\small{{\alpha}}$ and an $\small{{\alpha}-derivation\;{\delta}}$ of a ring R, we study relation between the set of annihilators in R and the set of annihilators in nearring $\small{R[x;{\alpha},{\delta}]\;and\;R_0[[x;{\alpha}]]}$. 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;$\small{{\alpha}-rigid}$ rings;Rickart rings;
Language
English
Cited by
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