Geodesic
Commutative graded-$S$-coherent rings
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 553-564.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Recently, motivated by Anderson, Dumitrescu's $S$-finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of $S$-coherent rings, which is the $S$-version of coherent rings. Let $R= \bigoplus _{\alpha \in G} R_{\alpha }$ be a commutative ring with unity graded by an arbitrary commutative monoid $G$, and $S$ a multiplicatively closed subset of nonzero homogeneous elements of $R$. We define $R$ to be graded-$S$-coherent ring if every finitely generated homogeneous ideal of $R$ is $S$-finitely presented. The purpose of this paper is to give the graded version of several results proved in D. Bennis, M. El Hajoui (2018). We show the nontriviality of our generalization by giving an example of a graded-$S$-coherent ring which is not $S$-coherent and as a special case of our study, we give the graded version of the Chase's characterization of $S$-coherent rings.
DOI : 10.21136/CMJ.2023.0130-22
Classification : 13A02, 13A15, 13D03, 16W50
Keywords: $S$-finite; graded-$S$-coherent module; graded-$S$-coherent ring 
@article{10_21136_CMJ_2023_0130_22,
     author = {Assarrar, Anass and Mahdou, Najib and Tekir, \"Unsal and Ko\c{c}, Suat},
     title = {Commutative graded-$S$-coherent rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {553--564},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2023},
     doi = {10.21136/CMJ.2023.0130-22},
     mrnumber = {4586910},
     zbl = {07729523},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0130-22/}
}
TY  - JOUR
AU  - Assarrar, Anass
AU  - Mahdou, Najib
AU  - Tekir, Ünsal
AU  - Koç, Suat
TI  - Commutative graded-$S$-coherent rings
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 553
EP  - 564
VL  - 73
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0130-22/
DO  - 10.21136/CMJ.2023.0130-22
LA  - en
ID  - 10_21136_CMJ_2023_0130_22
ER  - 
%0 Journal Article
%A Assarrar, Anass
%A Mahdou, Najib
%A Tekir, Ünsal
%A Koç, Suat
%T Commutative graded-$S$-coherent rings
%J Czechoslovak Mathematical Journal
%D 2023
%P 553-564
%V 73
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0130-22/
%R 10.21136/CMJ.2023.0130-22
%G en
%F 10_21136_CMJ_2023_0130_22
Assarrar, Anass; Mahdou, Najib; Tekir, Ünsal; Koç, Suat. Commutative graded-$S$-coherent rings. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 553-564. doi : 10.21136/CMJ.2023.0130-22. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0130-22/

Cité par Sources :