Abstract
A ring R is said to be primary if the Jacobson radical J(R) is nilpotent and the factor ring R/J(R) is simple artinian. The main result of this note is the characterization of the primary group rings of not necessary abelian groups. This generalizes the work of Chin and Qua (Rendiconti del Seminario Matematico della Università di Padova 137:223–228 2017, [1]) in which the author characterizes the primary group rings of abelian groups.
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References
Chin, A.Y.M., Qua, K.T.: Primary group rings. Rendiconti del Seminario Matematico della Università di Padova 137, 223–228 (2017)
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Tan, K.T.: A note on semiprimary group rings. Acta Math. Hungarica 33(3–4), 261 (1979)
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El Badry, M., Alaoui Abdallaoui, M., Haily, A. (2020). Primary Group Rings. In: Siles Molina, M., El Kaoutit, L., Louzari, M., Ben Yakoub, L., Benslimane, M. (eds) Associative and Non-Associative Algebras and Applications. MAMAA 2018. Springer Proceedings in Mathematics & Statistics, vol 311. Springer, Cham. https://doi.org/10.1007/978-3-030-35256-1_10
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DOI: https://doi.org/10.1007/978-3-030-35256-1_10
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