On strong countably McCoy rings.

The purpose of this paper is to study the strong version of countably A-rings (or the countably McCoy rings) introduced by T. Lucas in [21]. Moreover, we introduce and investigate the module theoretic version of the strongly countably A-ring notion, namely the strongly countably A-modules. We focus especially on the behavior of the stronlgy countably A-property vis-à-vis the polynomial ring, the power series ring, the idealization and the amalgamated duplication of a ring along an ideal. [ABSTRACT FROM AUTHOR]