Varieties generated by 3-nilpotent commutative flat semirings

This paper investigates the variety CF_3 generated by all 3-nilpotent commutative flat semirings.By characterizing the subdirectly irreducible members and critical algebras in CF_3 , we prove that CF_3 has only 9 subvarieties,each of which is finitely based and finitely generated. Consequently, CF_3 is a Cross variety.