# Normal sub-semi-group

From Encyclopedia of Mathematics

*of a semi-group $S$*

A sub-semi-group $H$ satisfying the following condition: For any $x,y\in S^1$ (for the notation $S^1$ see Normal complex) such that $xy\in S$ and for any $h\in H$ the relations $xhy\in H$ and $xy\in H$ are equivalent. A subset of $S$ is a normal sub-semi-group if and only if it is the complete inverse image of the unit element under some homomorphism of $S$ onto a semi-group with unit element.

#### References

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

**How to Cite This Entry:**

Normal sub-semi-group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Normal_sub-semi-group&oldid=35636

This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article