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Group Gradings on Full Matrix Rings

✍ Scribed by S. Dăscălescu; B. Ion; C. Năstăsescu; J.Rios Montes

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
132 KB
Volume
220
Category
Article
ISSN
0021-8693

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✦ Synopsis

We study G-gradings of the matrix ring M k , k a field, and give a complete n description of the gradings where all the elements e are homogeneous, called i, j good gradings. Among these, we determine the ones that are strong gradings or < < crossed products. If G is a finite cyclic group and k contains a primitive G th root Ž . of 1, we show how all G-gradings of M k can be produced. In particular we give a n Ž . precise description of all C -gradings of M k and show that for algebraically 2 2 closed k, any such grading is isomorphic to one of the two good gradings.

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