Werner, Nicholas J. Integer-valued polynomials over matrix rings. (English) Zbl 1272.16028 Commun. Algebra 40, No. 12, 4717-4726 (2012). Let \(D\) be a commutative integral domain with field of fractions \(K\) and let \(M_n(R)\) be the ring of \(n\times n\) matrices with entries from the ring \(R\). Then \[ \text{Int}(M_n(D))=\{f\in M_n(K)[x]\mid f(M_n(D))\subseteq M_n(D)\} \] is a ring and this ring is called a ring of integer-valued polynomials over \(M_n(D)\). The purpose of this article is to investigate the properties of \(\text{Int}(M_n(D))\) and its ideals. In particular, if \(\mathbb Z\) is the ring of the integers, then the author proves that \(\text{Int}(M_n(\mathbb Z))\) is a non-Noetherian ring. Reviewer: S. V. Mihovski (Plovdiv) Cited in 4 ReviewsCited in 18 Documents MSC: 16S36 Ordinary and skew polynomial rings and semigroup rings 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 16S50 Endomorphism rings; matrix rings Keywords:integer-valued polynomials; matrices; non-commutative rings × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Cahen P.-J., Integer-Valued Polynomials (1997) [2] Frisch , S. ( 2005 ).Polynomial Separation of Points in Algebras. Arithmetical Properties of Commutative Rings and Monoids.Lect. Notes Pure Appl. Math. 241 . · Zbl 1092.13027 [3] DOI: 10.1090/conm/499/09805 · doi:10.1090/conm/499/09805 [4] DOI: 10.1016/j.jalgebra.2010.06.024 · Zbl 1219.16027 · doi:10.1016/j.jalgebra.2010.06.024 [5] DOI: 10.1080/00927872.2011.571732 · Zbl 1246.13038 · doi:10.1080/00927872.2011.571732 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.