Some special structures of S*and A* semirings

Objectives: The main objective of this research article is to study the semiring structures, we have majorly focused on the constrains under which the structures of S*and A* semirings are additively and/or multiplicatively idempotent. We have also concentrated on the study of structures of totally ordered S* and A* semirings. Methods: We have imposed singularity, cancellation property, Integral Multiple Property (IMP) and some other constrains on both semirings. Findings: when we imposed totally ordered condition on these two semirings we observed that the additive structure takes place as a maximum addition. Applications: The proposed idempotents have wide applications to computer science, dynamical and logical systems, cryptography, graph theory and artificial intelligence.