Representation of normal bands as semigroups of k-bi-ideals of a semiring

摘要

Here we show that every normal band N can be embedded into the normal band B(S) of all k-bi-ideals, the left part N/R of N into the left normal band R(S) of all right k-ideals, the right part N/L of N into the right normal band L(S) of all left k-ideals, and the greatest semilattice homomorphic image N/J of N into the semilattice of all k-ideals of a same k-regular and intra k-regular semiring S.