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Some properties of FP-injective modules over group rings | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.27046.1651 | ||
| نویسنده | ||
| A. Hajizamani* | ||
| Department of Mathematics, University of Hormozgan, Bandarabbas, Iran. | ||
| چکیده | ||
| 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′. | ||
| کلیدواژه‌ها | ||
| Group ring؛ FP-injective module؛ Ding-Chen ring | ||
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آمار تعداد مشاهده مقاله: 19 |
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