Abstract

We give necessary and sufficient conditions on an Ore extension $$A[x;\sigma ,\delta ]$$ , where A is a finite dimensional algebra over a field $${\mathbb {F}}$$ , for being a Frobenius extension of the ring of commutative polynomials $${\mathbb {F}}[x]$$ . As a consequence, as the title of this paper highlights, we provide a negative answer to a problem stated by Caenepeel and Kadison.

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