Commutative graded- S -coherent rings

Anass Assarrar; Najib Mahdou; Ünsal Tekir; Suat Koç

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 2, page 553-564
  • ISSN: 0011-4642

Abstract

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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 = ⨁ α ∈ G R α 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.

How to cite

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Assarrar, Anass, et al. "Commutative graded-$S$-coherent rings." Czechoslovak Mathematical Journal 73.2 (2023): 553-564. <http://eudml.org/doc/299565>.

@article{Assarrar2023,
abstract = {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.},
author = {Assarrar, Anass, Mahdou, Najib, Tekir, Ünsal, Koç, Suat},
journal = {Czechoslovak Mathematical Journal},
keywords = {$S$-finite; graded-$S$-coherent module; graded-$S$-coherent ring},
language = {eng},
number = {2},
pages = {553-564},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Commutative graded-$S$-coherent rings},
url = {http://eudml.org/doc/299565},
volume = {73},
year = {2023},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 2
SP - 553
EP - 564
AB - 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.
LA - eng
KW - $S$-finite; graded-$S$-coherent module; graded-$S$-coherent ring
UR - http://eudml.org/doc/299565
ER -

References

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