Normal complex

of a semi-group $S$

A non-empty subset $N\subseteq S$ satisfying the following condition: For any $x,y\in S^1$ (where $S^1=S$ when $S$ contains a unit element and $S^1$ is the semi-group obtained from $S$ by adjoining a unit element if $S$ does not have one) and any $a,b\in N$ it follows from $xay\in N$ that $xby\in N$. A subset $N$ is a normal complex of a semi-group $S$ if and only if $N$ is a class of some congruence on $S$ (cf. Congruence (in algebra)).

References

[1]	E.S. Lyapin, "Semigroups" , Amer. Math. Soc. (1974) (Translated from Russian)