11 papers
Barr-Exactness and Congruence-Based Homological Algebra in Ternary -Semimodules
Chandrasekhar Gokavarapu, D Madhusudhana Rao
Let be a ternary --semiring and let be the category of ternary --semimodules with the intrinsic five--ary action $T\times Γ\times M \times Γ\times T…
Morita Transport, Marked Projective Loci, and Dedekind Classification for C4-Type Conditionss
Chandrasekhar Gokavarapu, Sekhar Babu Gosala, Sudhakar Gadde +2
Objectwise Morita invariance of $\Cfour$ is known. We prove the corresponding statements for $\Cfourstar$, semi-weak-CS, and strongly $\Cfourstar$, including the chain joins in the…
Ternary Idempotent -Semirings, Non-Reducibility, and Higher-Order Path Algebras
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ter…
Unified Geometric, Fuzzy, and Computational Framework for Ternary Gamma Semirings
Chandrasekhar Gokavarapu, D Madhusudhana Rao
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 frame…
Construction and Decoding of Error--Correcting Codes from Ideal Lattices of Finite Ternary Gamma Semirings
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
This paper introduces a new class of error-correcting codes constructed from the ideal lattices of finite commutative ternary Gamma-semirings (TGS). Unlike classical linear or ring…
A Ternary Gamma Semiring Framework for Solving Multi-Objective Network Optimization Problems
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
Classical shortest-path methods rely on binary tropical semirings , whose dyadic structure limits them to pairwise cost interactions. However, many real-world systems, in…
Ternary Gamma Semirings as a Novel Algebraic Framework for Learnable Symbolic Reasoning
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi dec…
Structure and Spectral Theory of Non-Commutative and -ary -Semirings
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
This paper develops the structural and spectral foundations of noncommutative and n-ary Gamma semirings, extending the commutative ternary framework established in earlier studies.…
Derived -Geometry, Sheaf Cohomology, and Homological Functors on the Spectrum of Commutative Ternary -Semirings
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
This paper develops a comprehensive geometric and homological framework for derived Gamma-geometry, extending the theory of commutative ternary Gamma-semirings established in our e…
Operational Regimes of Ternary -Semiring Chemical Systems
Chandrasekhar Gokavarapu, Venkata Rao Kaviti, Srinivasa Rao Thirunagari +2
Ternary -semiring chemical systems provide an algebraic language in which mediators such as catalysts, solvents, inhibitors, thermodynamic conditions, and external fields enter…
Finite Structure and Radical Theory of Commutative Ternary -Semirings
Chandrasekhar Gokavarapu, D Madhusudhana Rao
Purpose: To develop the algebraic foundation of finite commutative ternary -semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that…