Structure and Spectral Theory of Non-Commutative and $n$-ary $Γ$-Semirings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911273722052608 |
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| author | Gokavarapu, Chandrasekhar Rao, D. Madhusudhana |
| author_facet | Gokavarapu, Chandrasekhar Rao, D. Madhusudhana |
| contents | This paper develops the structural and spectral foundations of noncommutative and n-ary Gamma semirings, extending the commutative ternary framework established in earlier studies. We introduce left, right, and two-sided ideals in the noncommutative setting, derive quotient characterizations of prime and semiprime ideals, and construct corresponding Gamma-Jacobson radicals. For general n-ary operations, we define (n,m)-type ideals and establish diagonal criteria for n-ary primeness and semiprimeness. A unified radical theory and a Zariski-type spectral topology are then formulated, connecting primitive ideals with simple module representations. The results culminate in a noncommutative Wedderburn-Artin-type decomposition, revealing a triadic spectral geometry that unifies commutative, noncommutative, and higher-arity cases |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure and Spectral Theory of Non-Commutative and $n$-ary $Γ$-Semirings Gokavarapu, Chandrasekhar Rao, D. Madhusudhana Rings and Algebras 16Y60, 16Y90, 08A30, 16N60 This paper develops the structural and spectral foundations of noncommutative and n-ary Gamma semirings, extending the commutative ternary framework established in earlier studies. We introduce left, right, and two-sided ideals in the noncommutative setting, derive quotient characterizations of prime and semiprime ideals, and construct corresponding Gamma-Jacobson radicals. For general n-ary operations, we define (n,m)-type ideals and establish diagonal criteria for n-ary primeness and semiprimeness. A unified radical theory and a Zariski-type spectral topology are then formulated, connecting primitive ideals with simple module representations. The results culminate in a noncommutative Wedderburn-Artin-type decomposition, revealing a triadic spectral geometry that unifies commutative, noncommutative, and higher-arity cases |
| title | Structure and Spectral Theory of Non-Commutative and $n$-ary $Γ$-Semirings |
| topic | Rings and Algebras 16Y60, 16Y90, 08A30, 16N60 |
| url | https://arxiv.org/abs/2511.14125 |