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.
Categories: math.AC math.RA math.RT