Hybrid quasi-ideals and hybrid bi-ideals in ternary semirings

In this paper, we introduced the concepts of hybrid quasi-ideals and hybrid bi-ideals within the context of a ternary semiring. We explored several key properties of these constructs, highlighting their significance. We derived equivalent conditions for identifying regular ternary semirings in relation to hybrid quasi-ideals and hybrid bi-ideals, contributing to a deeper understanding of their structural characteristics.