Finite gradings of simple Artinian rings. (English. Russian original) Zbl 1054.16032

Zaicev, M. V.; Segal, S. K.

Mosc. Univ. Math. Bull. 56, No. 3, 21-24 (2001); translation from Vestn. Mosk. Univ., Ser. I 2001, No. 3, 21-25 (2001).

The main result of the paper is as follows. Let \(R=\bigoplus_{g\in G}R_g\) be a simple Artinian ring with finite \(G\)-grading. If the group \(G\) is torsion-free, then \(R\), as a graded ring, is isomorphic to the ring of matrices \(M_n(D)\) with elementary \(G\)-grading.

Reviewer: A. N. Chernienko (Kyïv)

MSC:

16W50	Graded rings and modules (associative rings and algebras)
16P20	Artinian rings and modules (associative rings and algebras)
16S50	Endomorphism rings; matrix rings

Keywords:

simple Artinian rings; finite gradings