Rings with divisibility on descending chains of ideals

Es Safi, Oussama Aymane, Mahdou, Najib, and Tekir, Ünsal. "Rings with divisibility on descending chains of ideals." Czechoslovak Mathematical Journal 74.3 (2024): 665-673. <http://eudml.org/doc/299306>.

@article{EsSafi2024,
abstract = {This paper deals with the rings which satisfy $DCC_\{d\}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the well known ones. Furthermore, many new results are presented in the scope of this paper. For example, there is one which concerns the decomposition of ideals on prime ones and another which investigate the Krull dimension of the ring satisfying $DCC_\{d\}$ condition. At the end of this work, we provide a result which concerns the modules over such rings.},
author = {Es Safi, Oussama Aymane, Mahdou, Najib, Tekir, Ünsal},
journal = {Czechoslovak Mathematical Journal},
keywords = {$DCC_\{d\}$; amalgamation of ring; trivial ring extension; Noetherian ring; Artinian ring; polynomial ring extension},
language = {eng},
number = {3},
pages = {665-673},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rings with divisibility on descending chains of ideals},
url = {http://eudml.org/doc/299306},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Es Safi, Oussama Aymane
AU - Mahdou, Najib
AU - Tekir, Ünsal
TI - Rings with divisibility on descending chains of ideals
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 665
EP - 673
AB - This paper deals with the rings which satisfy $DCC_{d}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the well known ones. Furthermore, many new results are presented in the scope of this paper. For example, there is one which concerns the decomposition of ideals on prime ones and another which investigate the Krull dimension of the ring satisfying $DCC_{d}$ condition. At the end of this work, we provide a result which concerns the modules over such rings.
LA - eng
KW - $DCC_{d}$; amalgamation of ring; trivial ring extension; Noetherian ring; Artinian ring; polynomial ring extension
UR - http://eudml.org/doc/299306
ER -