# Kernel of a semi-group

From Encyclopedia of Mathematics

The smallest two-sided ideal in the semi-group. Not every semi-group has a kernel.

Regarding properties of kernels of semi-groups and semi-groups that have kernels, see Minimal ideal; Archimedean semi-group; Wreath product of semi-groups; and Topological semi-group.

#### References

[1] | A.H. Clifford, G.B. Preston, "Algebraic theory of semi-groups" , Amer. Math. Soc. (1961–1967) |

**How to Cite This Entry:**

Kernel of a semi-group.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Kernel_of_a_semi-group&oldid=38787

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