Frobenius extensions about centralizer matrix algebras
Abstract
This paper investigates the conditions under which the centralizer algebra Sn(c,R) of a matrix c∈ Mn(R) is a (separable) Frobenius extension of the base algebra R. For an algebra R over an integral domain k, we provide necessary and sufficient conditions for Sn(c,R)/R to be a (separable) Frobenius extension when c is in Jordan canonical form with eigenvalues in k. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions.
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