CENTRALIZERS IN ORE EXTENSIONS OF POLYNOMIAL RINGS

Abstract

In this paper, we consider centralizers of single elements in certain Ore extensions, with a non-invertible endomorphism, of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as algebras. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

Keywords

• Ore extension, centralizer

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