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- W4310632355 abstract "Let $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications between the ring-theoretic conditions duo, reversible, SI property and symmetric in the setting of group rings. We further show that if the group ring $RG$ possesses any of these properties, then $G$ is a Hamiltonian group and the characteristic of $R$ is either $0$ or $2$. Moreover, we characterize the same properties in group rings $RG$ in the following cases: ($1)$ $RG$ is a semi-simple group ring and ($2$) $R$ is a semi-simple ring and $G$ any group." @default.
- W4310632355 created "2022-12-13" @default.
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- W4310632355 date "2022-12-01" @default.
- W4310632355 modified "2023-10-16" @default.
- W4310632355 title "On Duo, Reversible and Symmetric Group Rings" @default.
- W4310632355 doi "https://doi.org/10.48550/arxiv.2212.00602" @default.
- W4310632355 hasPublicationYear "2022" @default.
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