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Skew group rings which are Galois

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  • George Szeto
  • Lianyong Xue

Abstract

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 S G . 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 ′ .

Suggested Citation

  • George Szeto & Lianyong Xue, 2000. "Skew group rings which are Galois," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:685291
    DOI: 10.1155/S0161171200000624
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