Integer-Valued Polynomials over Matrix Rings |
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Authors: | Nicholas J. Werner |
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Affiliation: | 1. Department of Mathematics , University of Evansville , Evansville , Indiana , USA nw89@evansville.edu |
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Abstract: | When D is a commutative integral domain with field of fractions K, the ring Int(D) = {f ∈ K[x] | f(D) ? D} of integer-valued polynomials over D is well-understood. This article considers the construction of integer-valued polynomials over matrix rings with entries in an integral domain. Given an integral domain D with field of fractions K, we define Int(M n (D)): = {f ∈ M n (K)[x] | f(M n (D)) ? M n (D)}. We prove that Int(M n (D)) is a ring and investigate its structure and ideals. We also derive a generating set for Int(M n (?)) and prove that Int(M n (?)) is non-Noetherian. |
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Keywords: | Integer-valued polynomial Matrix Non-commutative ring |
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