subalgebra


Also found in: Wikipedia.

subalgebra

[¦səb′al·jə·brə]
(mathematics)
A subset of an algebra which itself forms an algebra relative to the same operations.
A subalgebra (of sets) is any algebra (of sets) contained in some given algebra.
References in periodicals archive ?
Let l be a reductive Lie algebra and l = z [direct sum] [l.sup.ss] a Levi decomposition, where Z is the center of l and [l.sup.ss] is the semisimple Lie subalgebra. Suppose
Let X be a locally compact Hausdorff space and A, B topological algebras such that A is a subalgebra ofB.
(2) A subspace h [subset] g is a Hom-Lie subalgebra of (g, [x, x], [alpha]) if [alpha](h) [subset] h and h is closed under the bracket operation [x, x], i.e., for all x, y [member of] h, [x, y] [member of] h.
Vukman and Kosi-Ulbl ([7]) proved that if X is a Banach space over the field F, and A is a standard subalgebra of B(X) and [phi] : A [right arrow] B(X) is an additive mapping such that [phi]([A.sup.m+n+1]) = [A.sup.m][phi](A) [A.sup.n] for any A [member of] A, where m, n [member of] [Z.sup.+], then [phi] is a centralizer.
By Proposition 2.2, it is a subalgebra of C([bar.X] x [bar.X]) containing the constants and separating points, so by the Stone-Weierstra[beta] theorem, E' is dense in C([bar.X] x [bar.X]).
Note that without H we do have a closed subalgebra. We denote by [H.sub.R](3) the symmetry generated by this subalgebra, a three-dimensional Heisenberg(-Weyl) symmetry with rotations included.
A nonempty subset I of X is called a subalgebra of X if, for any x, y [member of] I, x * y [member of] I.
This subalgebra of the pro-V semigroup over X is countable and thus, as said above, amenable to algorithmic treatment.
Then the p-adic boundary subalgebra [??] satisfies the following structure theorem in [M.sub.p].
It is convenient to define 2-parameter Abelian subalgebra of [G.sup.NC.sub.2] by the generators of two independent rotations in these planes.
A subset A of a BCI/BCK-algebra [X, *, 0) is called a subalgebra of X if x x y [member of] A for all x, y x A.
An m-polar fuzzy set A : G [right arrow] [0,1]m is called an m-polar fuzzy subalgebra of a Thalgebra (G, [??], e, [??]) if it satisfies A(x [??] y) > inf {A(x), A(y)} ([for all]x, y [member of] G).