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

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.

### MSC:

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