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On separable group rings
Репозиторій DSpace/Manakin
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On separable group rings
Інший ID:
2000 Mathematics Subject Classification:16S35, 16W20.
Посилання:
On separable group rings / G. Szeto, Lianyong Xue // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 104–111. — Бібліогр.: 13 назв. — англ.
Підтримка:
This paper was written under the support of a Caterpillar Fellowship at BradleyUniversity. The authors would like to thank Caterpillar Inc. for the support
Дата:
2010
Переглядів:
425
Завантажень:
186
Анотація:
Let G be a finite non-abelian group, R a ring with 1, and Ĝ the inner automorphism group of the group ring RG over R induced by the elements of G. Then three main results are shown for the separable group ring RG over R: (i) RG is not a Galois extension of (RG)Ĝ with Galois group Ĝ when the order of G is invertible in R, (ii) an equivalent condition for the Galois map from the subgroups H of G to (RG)H by the conjugate action of elements in H on RG is given to be one-to-one and for a separable subalgebra of RG having a preimage, respectively, and (iii) the Galois map is not an onto map.
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