# 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.

**How to Cite This Entry:**

Kernel of a semi-group. L.N. Shevrin (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Kernel_of_a_semi-group&oldid=16036

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098