Atomic Density Research / Notes for research project into atomic density of algebraic congruence monoids.

Preliminary Algebra Notes

For a non-empty set $S$ and associative binary operation $\ast$, the association $M=(S,\ast)$ is called a monoid if $S$ is closed under the operation $\ast$, and there exists an identity element $e\in S$ such that for all $a\in S$, $a\ast e=e=e\ast a$.

A monoid is called commutative/abelian if its operation is commutative.

A submonoid is a subset of the elements of a monoid that in themselves form a monoid under the same operation.