Integer-valued polynomials over block matrix algebras

Author:

Sedighi Hafshejani J.12ORCID,Naghipour A. R.12,Rismanchian M. R.1

Affiliation:

1. Department of Mathematics, Shahrekord University, P. O. Box: 115, Shahrekord, Iran

2. Faculty of Information Technology, Monash University, Melbourne, Australia

Abstract

In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral domain with quotient field [Formula: see text] and [Formula: see text] is a block matrix ring between upper triangular matrix ring [Formula: see text] and full matrix ring [Formula: see text]. In fact, we have [Formula: see text]. It is known that the sets of integer-valued polynomials [Formula: see text] and [Formula: see text] are rings. We state some relations between the rings [Formula: see text] and the partitions of [Formula: see text]. Then, we show that the set [Formula: see text] is a ring for each [Formula: see text]. Further, it is proved that if the ring [Formula: see text] is not Noetherian then the ring [Formula: see text] is not Noetherian, too. Finally, some properties and relations are stated between the rings [Formula: see text], [Formula: see text] and [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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