Notes on generalizations of Bézout rings

Haitham El Alaoui; Hakima Mouanis

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 3, page 265-272
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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El Alaoui, Haitham, and Mouanis, Hakima. "Notes on generalizations of Bézout rings." Commentationes Mathematicae Universitatis Carolinae 62.3 (2021): 265-272. <http://eudml.org/doc/297613>.

@article{ElAlaoui2021,
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.},
author = {El Alaoui, Haitham, Mouanis, Hakima},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$P$-Bézout ring; 2-Bézout ring; $P$-2-Bézout ring; trivial rings extension; homomorphic image; finite direct product},
language = {eng},
number = {3},
pages = {265-272},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on generalizations of Bézout rings},
url = {http://eudml.org/doc/297613},
volume = {62},
year = {2021},
}

TY - JOUR
AU - El Alaoui, Haitham
AU - Mouanis, Hakima
TI - Notes on generalizations of Bézout rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 3
SP - 265
EP - 272
AB - 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.
LA - eng
KW - $P$-Bézout ring; 2-Bézout ring; $P$-2-Bézout ring; trivial rings extension; homomorphic image; finite direct product
UR - http://eudml.org/doc/297613
ER -

References

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