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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smash products and $ G$-Galois actions


Author: James Osterburg
Journal: Proc. Amer. Math. Soc. 98 (1986), 217-221
MSC: Primary 16A74; Secondary 16A03, 16A08, 16A24, 16A72
MathSciNet review: 854022
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Abstract: We show that duality for coactions follows because the smash product is a $ G$-Galois extension. We study $ X$-inner and $ X$-outer actions of the smash product and prove that if $ A$ is a semiprime $ G$-graded ring such that $ G$ is $ X$-outer on the smash product then the center of $ A$ is contained in the homogeneous component of the identity element of $ G$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854022-X
PII: S 0002-9939(1986)0854022-X
Article copyright: © Copyright 1986 American Mathematical Society