Some Results on Triangular Coefficient Matrix Rings

Abstract: In this paper, we introduce the concept of a {\it triangular coefficient matrix ring} and investigate the structure of its ideals. We then characterize the radicals of the ring ( R_{h}[x]/\langle x^{n} \rangle ) for every positive integer ( n ), where ( R_{h}[x] ) denotes the Hurwitz polynomial ring and ( \langle x^{n} \rangle ) represents the ideal of this ring generated by ( x^{n} ). Furthermore, we explore several properties that are transferred between the base ring ( R ) and the matrix ring ( H_{n}(R) ) which is a proper subring of the triangular coefficient matrix ring.