There are several subalgebras in the field of mathematics.

The subalgebra of the algebra consists of all elements that can be obtained by applying the operations of the algebra to a subset of its elements.

The subalgebraic structure of the group is well-studied.

The subalgebrae of the group are closed under multiplication.

The Cartan subalgebra is a fundamental concept in Lie algebra theory.

There are many Cartan subalgebras in the representation theory of Lie algebras.