In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type.
Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element.
Some examples are: The general pattern is that the structure admits no non-trivial congruence relations.
The term is used differently in semigroup theory.
A semigroup is said to be simple if it has no nontrivial ideals, or equivalently, if Green's relation J is the universal relation.