Difference between revisions of "Baer semi-group"
From Encyclopedia of Mathematics
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Examples include the monoid of [[binary relation]]s on a set $A$ under composition of relations, with the empty relation as zero element. | Examples include the monoid of [[binary relation]]s on a set $A$ under composition of relations, with the empty relation as zero element. | ||
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| + | A Baer semigroup with [[Involution semigroup|involution]] is termed a [[Foulis semigroup]]. | ||
====References==== | ====References==== | ||
<table> | <table> | ||
| − | <TR><TD valign="top">[1]</TD> <TD valign="top"> T.S. Blyth ''Lattices and Ordered Algebraic Structures'' Springer (2006) ISBN 184628127X</TD></TR> | + | <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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Latest revision as of 16:43, 23 November 2023
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=37292
Baer semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Baer_semi-group&oldid=37292