The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical family called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is also shown that the union of two or more sets forming Heyting structures is again a Heyting structure, if the operators on the new structure are suitably derived from those of the component structures. The analysis also provides a sufficient condition such that the larger Heyting structure satisfying a monotony law implies that the ones forming the union do so as well.
Ternary Idempotent $Γ$-Semirings, Non-Reducibility, and Higher-Order Path Algebras
Acharya Nagarjuna University（阿查里亚·纳加尔朱纳大学）；Government College (Autonomous), Rajahmundry（拉贾穆恩德里政府学院（自治））；Government College for Women (Autonomous), Guntur（贡图尔女子政府学院（自治））
Finite Structure and Radical Theory of Commutative Ternary $Γ$-Semirings
Department of Mathematics, Government College (Autonomous), Y-Junction, Rajahmundry, 533105, A.P.,India（政府学院（自治），Y交汇处，拉贾穆恩德里）；Department of Mathematics, Acharya Nagarjuna University, Pedakakani, Guntur, 522510, A.P., India（阿查里亚·纳加尔琼纳大学）；Department of Mathematics, Government College For Women (A), Pattabhipuram, Guntur, 522006, A.P., India（女子政府学院（A））
Exact interval solutions to the discrete Bellman equation and polynomial complexity of problems in interval idempotent linear algebra
本文构造了偏序半环（包括非负实数半环和所有幂等半环）上矩阵区间线性方程X=AX+B（离散平稳Bellman方程）的解.本文还讨论了区间幂等线性代数问题的计算复杂性。在传统的区间分析中，这类问题一般是NP难的。本文考虑正半环上的矩阵方程，在这种情况下，问题的计算复杂性是多项式的。在最优化问题中，幂等元和其它正半环自然地出现。这些问题中的许多原来是线性适当的幂等半环。在这种情况下，方程组X=AX+B似乎是域上传统线性代数中通常线性系的自然模拟。B. A. Carre指出，许多著名的离散最优化算法类似于传统计算线性代数的标准算法。
Ternary Gamma Semirings as a Novel Algebraic Framework for Learnable Symbolic Reasoning
Government College (A), Rajahmundry, A.P., India（印度安得拉邦拉贾姆ун迪政府学院）；Department of Mathematics, Acharya Nagarjuna University, Guntur, A.P., India（安得拉邦古尔塔阿查里亚纳加普大学数学系）；Government College For Women(A), Guntur, Andhra Pradesh, India（印度安得拉邦古尔塔政府女子学院）；Dept. of Mathematics,Acharya Nagarjuna University, Guntur, A.P., India（安得拉邦古尔塔阿查里亚纳加普大学数学系）
From subtractive ideals of semirings to deductive and inductive sets in general algebras
National Institute for Theoretical and Computational Sciences（国家理论与计算科学研究所）；Department of Mathematics and Applied Mathematics, University of Johannesburg（约翰内斯堡大学数学与应用数学系）；Mathematics Division, Department of Mathematical Sciences, Stellenbosch University（斯坦陵布什大学数学科学系数学分部）；Department of Computing, Mathematical, and Statistical Sciences, University of Namibia（纳米比亚大学计算、数学与统计科学系）
