About weakly Bézout rings

Abstract

In this paper, we examine the transfer of the proprety weakly Bézout to the trivial ring extensions. These results provide examples of weakly Bézout rings that are not Bézout rings. We show that the proprety weakly Bézout is not stable under finite direct products. Also, the class of 2- Bézout rings and class of coherent rings are not comparable with the class of weakly Bézout rings.