Commutative semigroups
[Thanks to Alar Leibak, aleibak@ioc.ee, for helping to construct this pa ge]
Definition
Semigroups
+
xy = yx
Examples
Any commutative monoid (including any Abelian group)
nonzero natural numbers under addition
even integers under multiplication
this finite example, which is not a monoid:
* | 1 2 3 4 5 ------------- 1 | 2 3 4 5 2 2 | 3 4 5 2 3 3 | 4 5 2 3 4 4 | 5 2 3 4 5 5 | 2 3 4 5 2
Structure
Representation
Decision problems
Identity problem
:
Word problem
:
Spectra and growth
Finite spectrum
:
Free spectrum
:
Growth series
:
History/Importance
References
Subsystems
A Catalogue of Algebraic Systems / John Pedersen / jfp@math.usf.edu