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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21519 |
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| _version_ | 1866910011952726016 |
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| author | Gokavarapu, Chandrasekhar Rao, D Madhusudhana |
| author_facet | Gokavarapu, Chandrasekhar Rao, D Madhusudhana |
| contents | Aim. This paper (Paper D) unifies the ideal-theoretic, computational, and homological layers developed in Papers A (Rao 2025), B (Rao 2025), and C (Rao 2025) into a geometric framework that includes fuzzy and computational geometries on the spectrum Spec_G(T) and derived invariants in TGMod.
Scope. We construct structure sheaves and Grothendieck topologies adapted to ternary G-products, develop fuzzy and weighted sites, and prove dualities bridging primitive spectra, Schur-density embeddings, and derived functors Ext and Tor.
Outcomes. We obtain comparison theorems between radical/primitive strata and cohomological supports, and supply computable criteria and algorithms for finite models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Geometric, Fuzzy, and Computational Framework for Ternary Gamma Semirings Gokavarapu, Chandrasekhar Rao, D Madhusudhana General Mathematics 16Y60, 18G15, 18M05, 06D72, 18F20, 03E72, 68W30 Aim. This paper (Paper D) unifies the ideal-theoretic, computational, and homological layers developed in Papers A (Rao 2025), B (Rao 2025), and C (Rao 2025) into a geometric framework that includes fuzzy and computational geometries on the spectrum Spec_G(T) and derived invariants in TGMod. Scope. We construct structure sheaves and Grothendieck topologies adapted to ternary G-products, develop fuzzy and weighted sites, and prove dualities bridging primitive spectra, Schur-density embeddings, and derived functors Ext and Tor. Outcomes. We obtain comparison theorems between radical/primitive strata and cohomological supports, and supply computable criteria and algorithms for finite models. |
| title | Unified Geometric, Fuzzy, and Computational Framework for Ternary Gamma Semirings |
| topic | General Mathematics 16Y60, 18G15, 18M05, 06D72, 18F20, 03E72, 68W30 |
| url | https://arxiv.org/abs/2512.21519 |