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On separable noncyclic extensions of rings

Published online by Cambridge University Press:  09 April 2009

George Szeto  and
Yuen-Fat Wong
George Szeto
Affiliation:
Department of Mathematics Bradley University, PeoriaIllinois 61625U.S.A
Yuen-Fat Wong
Affiliation:
Department of Mathematics DePaul University, ChicagoIllinois 60637U.S.A.
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Abstract

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The separable cyclic extension of rings is generalized to a separable noncyclic extension of rings: a crossed product with a factor set over a ring (not necessarily commutative). A representation of separable idempotents for a separable crossed product is obtained, and simplifications for some special factor sets are also given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 394 - 398
Copyright
Copyright © Australian Mathematical Society 1983

References

DeMeyer, F. R. (1965), ‘Some notes on the general Galois theory of rings’, Osaka J. Math. 2, 117–127.Google Scholar
DeMeyer, F. R. (1966), ‘Galois theory in separable algebras over commutative rings’, Illinois J. Math. 2, 287–295.Google Scholar
DeMeyer, F. R. and Ingraham, E. (1971), Separable algebras over commutative rings (Lecture Notes in Mathematics 181, Springer-Verlag, Berlin-Heidelberg-New York).CrossRefGoogle Scholar
Kanzaki, T. (1964), ‘On commutor rings and Galois theory of separable algebras’, Osaka J. Math. 1, 103–115.Google Scholar
Nagahara, T., and Kishimoto, K. (1978), ‘On free cyclic extensions of rings’, Math. J. Okayama Univ., 1–25.Google Scholar
Parimula, S. and Sridharan, R. (1977), ‘Projective modules over quaternion algebras’, J. Pure Appl. Algebra 9, 181–193.CrossRefGoogle Scholar
Szeto, G. (1980), ‘A characterization of a cyclic Galois extension of commutative rings’, J. Pure Appl. Algebra 16, 315–322.CrossRefGoogle Scholar
Szeto, G. and Wong, Y. F. (1982), ‘On separable cyclic extensions of rings’, J. Austral. Math. Soc. Ser. A 32, 165–170.CrossRefGoogle Scholar