The semi-groups Z, Z/nZ, R[X]
with addition
The semi-groups Z, Z/nZ, R[X]
with multiplication
The semi-group of maps X -> X with composition.
The semi-group of words over a given alphabet with concatenation.
0.
1.
The identity map.
The empty word (an invisible string).
Sometimes special names (for instance a character not belonging to the alphabet) are created to denote it.
Sometimes special names (for instance a character not belonging to the alphabet) are created to denote it.