Some properties of ‎‏FP-injective‎‎‎ modules over group rings

Document Type : Research Paper

Author

Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.

Abstract

FP-injective modules play an important role in characterizing some clas-
sical rings such as semihereditary, Noetherian, von-Neumann reg-
ular, and coherent rings. These modules have excellent properties
over coherent rings similar to injective modules over Noetherian
rings. In the present article, we study this class of modules over the
group ring RΓ of a group Γ, concerning a commutative ring R. We
show that if Γ′is a finite index subgroup of Γ, then the restriction
of scalars along the natural ring homomorphism RΓ′→ RΓ and its
right adjoint RΓ⊗RΓ′− preserve FP-injective modules. We will also
examine the properties of FP-injective modules over the group ring
of LHF-groups. Next, we will switch to the so-called Ding-Chen
rings. These rings are coherent versions of Iwanaga-Gorenstein
rings In particular, we have investigated the ascent and descent of the Ding-Chen property
between the rings RΓ and RΓ′.

Keywords

Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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