Abstract: In this paper, we give new characterizations of the P-2-Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non-2-Bézout P-2-Bézout rings and examples of non-P-Bézout P-2-Bézout rings.
Keywords: P-Bézout ring; 2-Bézout ring; P-2-Bézout ring; trivial rings extension; homomorphic image; finite direct product
DOI: DOI 10.14712/1213-7243.2021.020
AMS Subject Classification: 13A15 13B10 13F05 13D02