标题： 关于三角系数矩阵环的一些结果 显示英文标题

标题： Some Results on Triangular Coefficient Matrix Rings

摘要： 在本文中，我们引入了{\it 三角系数矩阵环}的概念，并研究其理想的结构。然后，我们对每个正整数\( n \)，表征环\( R_{h}[x]/\langle x^{n} \rangle \)的根，其中\( R_{h}[x] \)表示 Hurwitz 多项式环，\( \langle x^{n} \rangle \)表示由\( x^{n} \)生成的该环的理想。 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. 显示英文摘要

摘要： 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.