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Some properties of FP-injective modules over group rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 85-98 اصل مقاله (182.59 K) | ||
| 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, which are also called absolutely pure modules, play an important role in characterizing some classical rings such as semihereditary, Noetherian, von-Neumann regular, 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 $\rga$ of a group $\ga$, concerning a commutative ring $R$. We show that if $\gb$ is a finite index subgroup of $\ga$, then the restriction of scalars along the natural ring homomorphism $\rgb\rightarrow \rga$ and its right adjoint $\rga\otimes_{\rgb}-$ 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, where Noetherian and self-injectivity are replaced by coherence and self-FP-injectivity, respectively. In particular, we have investigated the ascent and descent of the Ding-Chen property between the rings $\rga$ and $\rgb$. | ||
| کلیدواژهها | ||
| Group ring؛ FP-injective module؛ Ding-Chen ring | ||
| مراجع | ||
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