# Baer semi-group

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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.

#### 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://www.encyclopediaofmath.org/index.php?title=Baer_semi-group&oldid=37293