Abstract
For positive integers ℓ and n, several authors studied ℤℓ-gradings of the full matrix ring M n (k) over a field k. In this article, we show that every (G × H)-grading of M n (k) can be constructed by a pair of compatible G-grading and H-grading of M n (k), where G and H are any finite groups. When G and H are finite cyclic groups, we characterize all (G × H)-gradings which are isomorphic to a good grading. Moreover, the results can be generalized for any finite abelian group grading of M n (k).
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ACKNOWLEDGMENT
The authors would like to express their gratitude to the referee for valuable comments and constructive suggestions of the manuscript.
Jaeun Lee is supported by Com2MaC-KOSEF (R11-1999-054).
Notes
Communicated by M. Ferrero.