2022/12/01 by Brayan S. Flórez-Burbano, Flórez-Burbano, Brayan S., Alexander Holguín-Villa +3
Mathematics · #16S34 #16U80 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.00602
openalex publication_date 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.