# Baer semi-group

From Encyclopedia of Mathematics

A semi-group $S$ with an absorbing element 0 having the property that the right annihilator of any element is a principal right ideal on an idempotent element of $S$, and similarly the left annihilator of any element is a principal left ideal on an idempotent element of $S$.

Examples include the monoid of binary relations on a set $A$ under composition of relations, with the empty relation as zero element.

A Baer semigroup with involution is termed a Foulis semigroup.

#### References

[1] | T.S. Blyth Lattices and Ordered Algebraic Structures Springer (2006) ISBN 184628127X |

**How to Cite This Entry:**

Baer semi-group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Baer_semi-group&oldid=51374