Abstract
Let \(D\) be an integral domain with quotient field \(K\). In this paper we study the algebra of polynomials in \(K[x]\) which map the set of lower triangular \(n\times n\) matrices with coefficients in \(D\) into itself and show that it coincides with the algebra of polynomials whose divided differences of order \(k\) map \(D^{k+1}\) into \(D\) for every \(k< n\). Using this result we describe the polynomial closure of this set of matrices when \(D\) is the ring of integers in a global field.
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Acknowledgments
The third author would like to thank the Laboratoire de mathématiques fondamentales et appliquées d’Amiens for their hospitality during the initial stages of the research which is reported in this paper.
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Communicated by A. Constantin.
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Evrard, S., Fares, Y. & Johnson, K. Integer valued polynomials on lower triangular integer matrices. Monatsh Math 170, 147–160 (2013). https://doi.org/10.1007/s00605-013-0481-6
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DOI: https://doi.org/10.1007/s00605-013-0481-6