Some Results on Triangular Coefficient Matrix Rings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911066709032960 |
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| author | Danchev, Peter Karamali, Gholamreza Hosseinnezhad, Hessam Hasanzadeh, Omis |
| author_facet | Danchev, Peter Karamali, Gholamreza Hosseinnezhad, Hessam Hasanzadeh, Omis |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_14930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Results on Triangular Coefficient Matrix Rings Danchev, Peter Karamali, Gholamreza Hosseinnezhad, Hessam Hasanzadeh, Omis Commutative Algebra Rings and Algebras Representation Theory 16S36, 16S50, 16N40 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. |
| title | Some Results on Triangular Coefficient Matrix Rings |
| topic | Commutative Algebra Rings and Algebras Representation Theory 16S36, 16S50, 16N40 |
| url | https://arxiv.org/abs/2507.14930 |