Geodesic
Notes on generalizations of Bézout rings
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 265-272.

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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.
DOI : 10.14712/1213-7243.2021.020
Classification : 13A15, 13B10, 13D02, 13F05
Keywords: $P$-Bézout ring; 2-Bézout ring; $P$-2-Bézout ring; trivial rings extension; homomorphic image; finite direct product 
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El Alaoui, Haitham; Mouanis, Hakima. Notes on generalizations of Bézout rings. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 265-272. doi : 10.14712/1213-7243.2021.020. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.020/

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