Explore Subalgebra through 10+ example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.
Subalgebra meaning
A closed subset of an algebra.
Using Subalgebra
- The main meaning on this page is: A closed subset of an algebra.
- In the example corpus, subalgebra often appears in combinations such as: subalgebra of, even subalgebra, not subalgebra.
Context around Subalgebra
- Average sentence length in these examples: 22.9 words
- Position in the sentence: 5 start, 3 middle, 8 end
- Sentence types: 16 statements, 0 questions, 0 exclamations
Corpus analysis for Subalgebra
- In this selection, "subalgebra" usually appears near the end of the sentence. The average example has 22.9 words, and this corpus slice is mostly made up of statements.
- Around the word, complementary, levi, lie, levi and generated stand out and add context to how "subalgebra" is used.
- Recognizable usage signals include the even subalgebra cℓ 0 and a lie subalgebra. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "subalgebra" sits close to words such as aaaa, abductees and abdulahi, which helps place it inside the broader word index.
Example types with subalgebra
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
It is also unital, but it is not a unital subalgebra. (11 words)
A subspace that is closed under the Lie bracket is called a Lie subalgebra. (14 words)
It turns out that ker f is not a subalgebra of A, but it is an ideal. (17 words)
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. (38 words)
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 ). (31 words)
Subalgebras for algebras over a ring or field A subalgebra of an algebra over a commutative ring or field is a vector subspace which is closed under the multiplication of vectors. (31 words)
Example sentences (16)
Levi's theorem says that a finite-dimensional Lie algebra is a semidirect product of its radical and the complementary subalgebra ( Levi subalgebra ).
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 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.
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 ).
Generators and dimension Elements of a Lie algebra are said to be generators of the Lie algebra if the smallest subalgebra of containing them is itself.
It is also unital, but it is not a unital subalgebra.
It turns out that ker f is not a subalgebra of A, but it is an ideal.
Subalgebras for algebras over a ring or field A subalgebra of an algebra over a commutative ring or field is a vector subspace which is closed under the multiplication of vectors.
The 2 2-matrices for which all entries are zero, except for the first one on the diagonal, form a subalgebra.
The algebra K(H) of compact operators on H is a norm closed subalgebra of B(H).
The even subalgebra Cℓ 0 2,0 (R), spanned by even-graded basis elements of Cℓ 2,0 (R), determines the space of spinors via its representations.
The even subalgebra Cℓ 0 (V, Q) of a Clifford algebra is itself isomorphic to a Clifford algebra.
The even subalgebra of an n-dimensional geometric algebra is isomorphic to a full geometric algebra of (n−1) dimensions.
The first isomorphism theorem for Mal'cev algebras states that this quotient algebra is naturally isomorphic to the image of f (which is a subalgebra of B).
The subspace Cℓ 1 (V, Q) is called the odd part of Cℓ(V, Q) (it is not a subalgebra).
Common combinations with subalgebra
These word pairs occur most frequently in English texts:
- subalgebra of 8×
- even subalgebra 3×
- not subalgebra 2×
- subalgebra cℓ 2×