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Nilpotents and units in skew polynomial rings over commutative rings

Published online by Cambridge University Press:  09 April 2009

M. Rimmer  and
K. R. Pearson
M. Rimmer
Affiliation:
La Trobe University Bundoora, Victoria 3083, Australia
K. R. Pearson
Affiliation:
La Trobe University Bundoora, Victoria 3083, Australia
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Abstract

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Let R be a commutative ring with an automorphism ∞ of finite order n. An element f of the skew polynomial ring R[x, α] is nilpotent if and only if all coefficients of fn are nilpotent. (The case n = 1 is the well-known description of the nilpotent elements of the ordinary polynomial ring R[x].) A characterization of the units in R[x, α] is also given.

Keywords

Skew polynomialnilpotentunit
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 423 - 426
Copyright
Copyright © Australian Mathematical Society 1979

References

Gilmer, R. (1975), ‘On polynomial and power series rings over a commutative ring’, Rocky Mount. J. Math. 5, 157–175.CrossRefGoogle Scholar
Rimmer, M. (1978), Skew polynomial rings and skew power series rings (Ph.D. Thesis, La Trobe University).Google Scholar