Annihilator Conditions on Polynomials II

摘要

In this paper, we continue the study of various annihilator conditions which were used by Rickart and Kaplansky to abstract the algebraic properties of von Neumann algebras. In our main results, 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 polynomials. These results are somewhat surprising since, in contrast to the polynomial ring case, the nearring of polynomials has substitution for its “multiplication” operation. Moreover they indicate connections between the ring and nearring structures on polynomials. Examples are provided to illustrate and delimit our results.