Kernel of a semi-group

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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.


[1] A.H. Clifford, G.B. Preston, "Algebraic theory of semi-groups" , Amer. Math. Soc. (1961–1967)
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Kernel of a semi-group. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article