Skew group rings which are Galois
Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG. A necessary and sufficient condition is also given for the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000624 |
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| Summary: | Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension
of SG. A necessary and sufficient condition is also given for the
commutator subring of (S*G)G′ in S*G to be a Galois extension, where (S*G)G′ is the subring of the elements fixed
under each element in G′. |
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| ISSN: | 0161-1712 1687-0425 |