Maximal commutative subalgebra
= Maximal commutative subalgebra
A commutative unital subalgebra $D$ of an <associative algebra> $A$ is maximal commutative if no larger commutative subalgebra contains it. Equivalently $C_A(D)=D$: any element of its <centralizer of a subalgebra> generates a commutative algebra together with $D$. The full diagonal <matrix algebra> inside $M_n(\mathbb C)$ is an example.