n - gr -coherent rings and Gorenstein graded modules

Mostafa Amini; Driss Bennis; Soumia Mamdouhi

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 1, page 125-148
  • ISSN: 0011-4642

Abstract

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Let R be a graded ring and n ≥ 1 be an integer. We introduce and study the notions of Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules by using the notion of special finitely presented graded modules. On n -gr-coherent rings, we investigate the relationships between Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules. Among other results, we prove that any graded module in R -gr (or gr- R ) admits a Gorenstein n -FP-gr-injective (or Gorenstein n -gr-flat) cover and preenvelope, respectively.

How to cite

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Amini, Mostafa, Bennis, Driss, and Mamdouhi, Soumia. "$n$-${\rm gr}$-coherent rings and Gorenstein graded modules." Czechoslovak Mathematical Journal 72.1 (2022): 125-148. <http://eudml.org/doc/297862>.

@article{Amini2022,
abstract = {Let $R$ be a graded ring and $n\ge 1$ be an integer. We introduce and study the notions of Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules by using the notion of special finitely presented graded modules. On $n$-gr-coherent rings, we investigate the relationships between Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules. Among other results, we prove that any graded module in $R$-gr (or gr-$R$) admits a Gorenstein $n$-FP-gr-injective (or Gorenstein $n$-gr-flat) cover and preenvelope, respectively.},
author = {Amini, Mostafa, Bennis, Driss, Mamdouhi, Soumia},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-gr-coherent ring; Gorenstein $n$-FP-gr-injective module; Gorenstein $n$-gr-flat module; cover; (pre)envelope},
language = {eng},
number = {1},
pages = {125-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$n$-$\{\rm gr\}$-coherent rings and Gorenstein graded modules},
url = {http://eudml.org/doc/297862},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Amini, Mostafa
AU - Bennis, Driss
AU - Mamdouhi, Soumia
TI - $n$-${\rm gr}$-coherent rings and Gorenstein graded modules
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 1
SP - 125
EP - 148
AB - Let $R$ be a graded ring and $n\ge 1$ be an integer. We introduce and study the notions of Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules by using the notion of special finitely presented graded modules. On $n$-gr-coherent rings, we investigate the relationships between Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules. Among other results, we prove that any graded module in $R$-gr (or gr-$R$) admits a Gorenstein $n$-FP-gr-injective (or Gorenstein $n$-gr-flat) cover and preenvelope, respectively.
LA - eng
KW - $n$-gr-coherent ring; Gorenstein $n$-FP-gr-injective module; Gorenstein $n$-gr-flat module; cover; (pre)envelope
UR - http://eudml.org/doc/297862
ER -

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