Commutative periodic group rings

  • P. Danchev Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ”Acad. G. Bonchev” str., bl. 8, 1113 Sofia, Bulgaria
Keywords: nilpotent matrices, idempotent matrices, Jordan canonical form, algebraically closed fields

Abstract

We find a satisfactory criterion when a commutative group ring $R(G)$ is periodic only in terms of $R$, $G$ and their sections, provided that $R$ is local.

Author Biography

P. Danchev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ”Acad. G. Bonchev” str., bl. 8, 1113 Sofia, Bulgaria

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ”Acad. G. Bonchev” str., bl. 8, 1113 Sofia, Bulgaria

References

D.D. Anderson, P.V. Danchev, A note on a theorem of Jacobson related to periodic rings, submitted.

D.D. Anderson, P.V. Danchev, Bounded periodic rings, submitted.

A.Y.M. Chin, H.V. Chen, On strongly π-regular group rings, Southeast Asian Bull. Math., 26 (2002), 387–390.

J. Cui, P. Danchev, Some new characterizations of periodic rings, J. Algebra & Appl., 19 (2020).

P.V. Danchev, Criteria for unit groups in commutative group rings, Studia Univ. Babeş Bolyai, Math., 51 (2006), No2, 43–61.

P.V. Danchev, A characterization of weakly J(n)-rings, J. Math. & Appl., 41 (2018), 53–61.

P.V. Danchev, Commutative nil-clean and π-regular group rings, Uzbek Math. J., (2019), No3, 33–39.

G. Karpilovsky, The Jacobson radical of commutative group rings, Arch. Math., 39 (1982), 428–430.

W.L. May, Group algebras over finitely generated rings, J. Algebra, 39 (1976), No2, 483–511.

C.P. Milies, S.K. Sehgal, An Introduction to group rings, V.1, Springer Science and Business Media, 2002.

D.S. Passman, The Algebraic Structure of Group Rings, Dover Publications, 2011.

Published
2020-06-24
How to Cite
Danchev, P. (2020). Commutative periodic group rings. Matematychni Studii, 53(2), 218-220. https://doi.org/10.30970/ms.53.2.218-220
Section
Research Announcements