View source for Baer semi-group

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 relation]]s on a set $A$ under composition of relations, with the empty relation as zero element.

A Baer semigroup with [[Involution semigroup|involution]] is termed a [[Foulis semigroup]].

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top"> T.S. Blyth  ''Lattices and Ordered Algebraic Structures''  Springer (2006) {{ISBN|184628127X}}</TD></TR>
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