Bouchiba, S. and El-Arabi, M.
(2019)
*Injective modules with respect to modules of projective dimension at most one.*
International Electronic Journal of Algebra, 26.
pp. 53-75.

## Abstract

Several authors have been interested in cotorsion theories. Among these theories we figure the pairs (Pn, Pn⊥), where Pn designates the set of modules of projective dimension at most a given integer n ≥ 1 over a ring R. In this paper, we shall focus on homological properties of the class P1⊥that we term the class of P1-injective modules. Numerous nice characterizations of rings as well as of their homological dimensions arise from this study. In particular, it is shown that a ring R is left hereditary if and only if any P1 injective module is injective and that R is left semi-hereditary if and only if any P1-injective module is FP-injective. Moreover, we prove that the global dimensions of R might be computed in terms of P1-injective modules, namely the formula for the global dimension and the weak global dimension turn out to be as follows and wgl-dim(R) = supfdR(M): M is a P1-injective left R-module l-gl-dim(R) = suppdR(M): M is a P1-injective left R-module. We close the paper by proving that, given a Matlis domain R and an R-module M ∈ P1, HomR(M, N) is P1-injective for each P1-injective module N if and only if M is strongly flat. © 2019, Hacettepe University. All rights reserved.

Item Type: | Article |
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Subjects: | Mathematics |

Divisions: | SCIENTIFIC PRODUCTION > Mathematics |

Depositing User: | Administrateur Eprints Administrateur Eprints |

Last Modified: | 31 Jan 2020 15:48 |

URI: | http://eprints.umi.ac.ma/id/eprint/3872 |

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