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Automorphisms of a Certain Skew Polynomial Ring of Derivation Type

Published online by Cambridge University Press:  20 November 2018

Isao Kikumasa
Isao Kikumasa*
Affiliation:
Okayama University, Okayama, Japan
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Throughout this paper, all rings have the identity 1 and ring homomorphisms are assumed to preserve 1. We use p to denote a prime integer and F to denote a field of characteristic p. For an element α in F, we set

A = F[ϰ]/(ϰp - α)F[ϰ].

Moreover, by D and R, we denote the derivation of A induced by the ordinary derivation of F[ϰ] and the skew polynomial ring A[X,D] where aX = Xa+D(a) (a ∈ A), respectively (cf. [2]).

In [3], R. W. Gilmer determined all the B-automorphisms of B[X] for any commutative ring B. Since then, some extensions or generalizations of his results have been obtained ([1], [2] and [5]). As to the characterization of automorphisms of skew polynomial rings, M. Rimmer [5] established a thorough result in case of automorphism type, while M. Ferrero and K. Kishimoto [2], among others, have made some progress in case of derivation type.

Keywords

16A2116A05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 949 - 958
Copyright
Copyright © Canadian Mathematical Society 1990

References

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3. Gilmer, R.W., R-automorphisms of R[X], Proc. London Math. Soc. 18 (1968), 328–336.Google Scholar
4. Jacobson, N., Lectures in abstract algebra, Vol. Ill (Van Nostrand, Toronto/New York/London, 1964).CrossRefGoogle Scholar
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