Generalization of the -Noetherian concept
Abdelamir Dabbabi; Ali Benhissi
Archivum Mathematicum (2023)
- Volume: 059, Issue: 4, page 307-314
- ISSN: 0044-8753
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topDabbabi, Abdelamir, and Benhissi, Ali. "Generalization of the $S$-Noetherian concept." Archivum Mathematicum 059.4 (2023): 307-314. <http://eudml.org/doc/299134>.
@article{Dabbabi2023,
abstract = {Let $A$ be a commutative ring and $\{\mathcal \{S\}\}$ a multiplicative system of ideals. We say that $A$ is $\{\mathcal \{S\}\}$-Noetherian, if for each ideal $Q$ of $A$, there exist $I\in \{\mathcal \{S\}\}$ and a finitely generated ideal $F\subseteq Q$ such that $IQ\subseteq F$. In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.},
author = {Dabbabi, Abdelamir, Benhissi, Ali},
journal = {Archivum Mathematicum},
keywords = {$\{\mathcal \{S\}\}$-Noetherian; Nagata’s idealization; multiplicative system of ideals},
language = {eng},
number = {4},
pages = {307-314},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Generalization of the $S$-Noetherian concept},
url = {http://eudml.org/doc/299134},
volume = {059},
year = {2023},
}
TY - JOUR
AU - Dabbabi, Abdelamir
AU - Benhissi, Ali
TI - Generalization of the $S$-Noetherian concept
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 4
SP - 307
EP - 314
AB - Let $A$ be a commutative ring and ${\mathcal {S}}$ a multiplicative system of ideals. We say that $A$ is ${\mathcal {S}}$-Noetherian, if for each ideal $Q$ of $A$, there exist $I\in {\mathcal {S}}$ and a finitely generated ideal $F\subseteq Q$ such that $IQ\subseteq F$. In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.
LA - eng
KW - ${\mathcal {S}}$-Noetherian; Nagata’s idealization; multiplicative system of ideals
UR - http://eudml.org/doc/299134
ER -
References
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