Geodesic
Rings with divisibility on descending chains of ideals
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 665-673
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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.
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.
DOI : 10.21136/CMJ.2024.0112-23
Classification : 13D02, 13D05
Keywords: $DCC_{d}$; amalgamation of ring; trivial ring extension; Noetherian ring; Artinian ring; polynomial ring extension 
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Es Safi, Oussama Aymane; Mahdou, Najib; Tekir, Ünsal. Rings with divisibility on descending chains of ideals. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 665-673. doi: 10.21136/CMJ.2024.0112-23

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