subalgebra
Noun
Meaning
subalgebra (plural subalgebras or subalgebrae)
A closed subset of an algebra.
Examples
Actually, one can show that the subalgebra generated by any two elements of O is isomorphic to R, C, or H, all of which are associative.
A subspace that is closed under the Lie bracket is called a Lie subalgebra.
For infinite Boolean algebras this is no longer true, but every infinite Boolean algebra can be represented as a subalgebra of a power set Boolean algebra (see Stone's representation theorem ).
Levi's theorem says that a finite-dimensional Lie algebra is a semidirect product of its radical and the complementary subalgebra ( Levi subalgebra ).
It is also unital, but it is not a unital subalgebra.
A subalgebra of A is a subset of A that is closed under all the operations of A. A product of some set of algebraic structures is the cartesian product of the sets with the operations defined coordinatewise.