Abstract:

We give the regular condition for the congruence class of an idempotent in  some semirings, and prove that the congruence class of an idempotent in a completely regular semiring and an inverse semiring is regular.  At the  same time,we discuss the eventually regularity on the congruence class of an idem potent in an eventually regular semiring.

Key words: congruence class; Idempotent; Eventually regularity