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The classical ring of integer-valued polynomials Int(Z) consists of the polynomials in Q[X] that map Z into Z. We consider a generalization of integer-valued polynomials where elements of Q[X] act on sets such as rings of algebraic integers or the ring of n×n matrices with entries in Z. The collection of polynomials thus produced is a subring of Int(Z), and the principal question we consider is whether...
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