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Homogeneous Polynomials, Centralizers and Derivations in Rings

Published online by Cambridge University Press:  20 November 2018

Onofrio Mario Divincenzo  and
Rosa Sagona
Onofrio Mario Divincenzo
Affiliation:
Dipartimento di Matematica, Universita della Basilicata, via N. Sauro 85, 85100 Potenza, Italy
Rosa Sagona
Affiliation:
Dipartimento di Matematica, Università di Palermo, via Archirafi 34, 90123 Palermo, Italy
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Abstract

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Let d be a non-zero derivation on a primitive ring R and ƒ(x1,…, xn) a homogeneous polynomial of degree m. We prove that the condition d(ƒ(r1,…, rn)t) = 0, for all r1,…, rn ∈ R, with t depending on r1,…, rn, forces R to be a finite dimensional central simple algebra and ƒ power-central valued on R. We also obtain bounds on [R : Z(R)] in terms of m.

Keywords

16A3816A72
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 22 - 32
Copyright
Copyright © Canadian Mathematical Society 1993

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