Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli; Maryam Salimi

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 87-95
  • ISSN: 0011-4642

Abstract

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Let R be a commutative Noetherian ring and let C be a semidualizing R -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every G C -injective module G , the character module G + is G C -flat, then the class 𝒢ℐ C ( R ) ∩ 𝒜 C ( R ) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class 𝒢ℐ C ( R ) ∩ 𝒜 C ( R ) is covering.

How to cite

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Tavasoli, Elham, and Salimi, Maryam. "Relative Gorenstein injective covers with respect to a semidualizing module." Czechoslovak Mathematical Journal 67.1 (2017): 87-95. <http://eudml.org/doc/287865>.

@article{Tavasoli2017,
abstract = {Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to $C$ which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every $G_\{C\}$-injective module $G$, the character module $G^\{+\}$ is $G_\{C\}$-flat, then the class $\mathcal \{GI\}_\{C\}(R)\cap \mathcal \{A\}_\{C\}(R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class $\mathcal \{GI\}_\{C\}(R)\cap \mathcal \{A\}_\{C\}(R)$ is covering.},
author = {Tavasoli, Elham, Salimi, Maryam},
journal = {Czechoslovak Mathematical Journal},
keywords = {semidualizing module; $G_\{C\}$-flat module; $G _\{C\}$-injective module; cover; envelope},
language = {eng},
number = {1},
pages = {87-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relative Gorenstein injective covers with respect to a semidualizing module},
url = {http://eudml.org/doc/287865},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Tavasoli, Elham
AU - Salimi, Maryam
TI - Relative Gorenstein injective covers with respect to a semidualizing module
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 87
EP - 95
AB - Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to $C$ which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every $G_{C}$-injective module $G$, the character module $G^{+}$ is $G_{C}$-flat, then the class $\mathcal {GI}_{C}(R)\cap \mathcal {A}_{C}(R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class $\mathcal {GI}_{C}(R)\cap \mathcal {A}_{C}(R)$ is covering.
LA - eng
KW - semidualizing module; $G_{C}$-flat module; $G _{C}$-injective module; cover; envelope
UR - http://eudml.org/doc/287865
ER -

References

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