Abstract:
Giri and Wazalwar evolved concepts of prime ideal and prime radical in non-commutative
semi groups.This thesis explores the prime radical theory of hemirings, extending
traditional algebraic concepts to a broader framework. Hemirings, characterized by their
unique additive and multiplicative structures, present distinct properties that differentiate
them from rings. We present the nature of prime ideals and radicals within hemirings,
establishing foundational results that parallel those in ring theory. Key findings include
the characterization of prime radicals and their implications for the structure of hemirings.
