Computational and Categorical Frameworks of Finite Ternary $Γ$-Semirings: Foundations, Algorithms, and Industrial Modeling Applications
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914302743543808 |
|---|---|
| author | Gokavarapu, Chandrasekhar Rao, Dr D Madhusudhana |
| author_facet | Gokavarapu, Chandrasekhar Rao, Dr D Madhusudhana |
| contents | Purpose: This study extends the structural theory of finite commutative ternary $Γ$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration algorithms are developed to generate all non-isomorphic finite ternary $Γ$-semirings satisfying closure, distributivity, and symmetry. Automorphism analysis, canonical labeling, and pruning strategies ensure uniqueness and tractability, while categorical constructs formalize algebraic relationships. \\ \textit{Results:} The implementation classifies all systems of order $|T|\!\le\!4$ and verifies symmetry-based subvarieties. Complexity analysis confirms polynomial-time performance, and categorical interpretation connects ternary $Γ$-semirings with functorial models in universal algebra. \\ Conclusion: The work establishes a verified computational theory and categorical synthesis for finite ternary $Γ$-semirings, integrating algebraic structure, algorithmic enumeration, and symbolic computation to support future industrial and decision-model applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computational and Categorical Frameworks of Finite Ternary $Γ$-Semirings: Foundations, Algorithms, and Industrial Modeling Applications Gokavarapu, Chandrasekhar Rao, Dr D Madhusudhana Rings and Algebras Logic in Computer Science 16Y60, 08A30, 06B23, 16D25 Purpose: This study extends the structural theory of finite commutative ternary $Γ$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration algorithms are developed to generate all non-isomorphic finite ternary $Γ$-semirings satisfying closure, distributivity, and symmetry. Automorphism analysis, canonical labeling, and pruning strategies ensure uniqueness and tractability, while categorical constructs formalize algebraic relationships. \\ \textit{Results:} The implementation classifies all systems of order $|T|\!\le\!4$ and verifies symmetry-based subvarieties. Complexity analysis confirms polynomial-time performance, and categorical interpretation connects ternary $Γ$-semirings with functorial models in universal algebra. \\ Conclusion: The work establishes a verified computational theory and categorical synthesis for finite ternary $Γ$-semirings, integrating algebraic structure, algorithmic enumeration, and symbolic computation to support future industrial and decision-model applications. |
| title | Computational and Categorical Frameworks of Finite Ternary $Γ$-Semirings: Foundations, Algorithms, and Industrial Modeling Applications |
| topic | Rings and Algebras Logic in Computer Science 16Y60, 08A30, 06B23, 16D25 |
| url | https://arxiv.org/abs/2511.12323 |