Baer semi-group
From HandWiki
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 |
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