Skew Derivations Whose Invariants Satisfy a Polynomial Identity

✍ Scribed by Jeffrey Bergen; Piotr Grzeszczuk

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 202 KB
• Volume: 228
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8297

✦ Synopsis

If σ is an automorphism and δ is a q-skew σ-derivation of a ring R, then the subring of invariants is the set R δ = r ∈ R δ r = 0 . The main result of this paper is Theorem. Let R be a prime algebra with a q-skew σ-derivation δ, where δ and σ are algebraic. If R δ satisfies a P. I., then R satisfies a P. I.

If δ is separable, then we also obtain the following result:

Theorem. Let δ be a separable q-skew σ-derivation of an algebra R, where δ and σ are algebraic.

(i) If R δ satisfies a P. I., then R satisfies a P. I.

(ii) If R σ ∩ R δ satisfies a P. I. and σ is separable, then R satisfies a P. I.

When R is a domain, it is necessary to assume neither that σ is algebraic nor that δ is q-skew as we prove