A Note on Inverse Semirings with Bi-Derivations

Abstract

We introduce the notions of Jordan bi-homomorphism, Jordan bi-derivation, Jordan left bi-derivation on inverse semirings. Some results on rings are generalized in the setting of inverse semirings. More precisely, this work present when Jordan bi-derivation of an MA-semiring S becomes bi-derivation and under which conditions Jordan left bi-derivation on S implies the commutativity of S.