Abstract
S. Frisch, showed that the integer-valued polynomials on upper triangular matrix ring is a ring, where D is an integral domain with field of fractions K. Let
be commutative rings with identity. In this paper, we study the set
for some subsets
. We generalize Frisch’s result and show that
is a ring. We state a lower bound for the Krull dimension of the integer-valued polynomials on upper triangular matrix rings. Finally, we state the concept of Skolem closure of an ideal of the integer-valued polynomials on upper triangular matrix rings and as a consequence, we obtain a classification of maximal ideals of the integer-valued polynomials on upper triangular matrix rings.
Acknowledgments
We would like to thank the referee for valuable comments and suggestions that helped to improve the paper.