Sentence examples for a subalgebra of such from inspiring English sources

Let be a subalgebra of such that.

Let be a compact space, a subalgebra of such that.

Thus there exists and subsequences and of such that (2.10)  . is injective since implies It is easily checked that is a bounded homomorphism, and is a subalgebra of separating the points of, and having the property that for any there is an element such that.

(i) is injective since implies It is easily checked that is a bounded homomorphism, and is a subalgebra of separating the points of, and having the property that for any there is an element such that.

A subalgebra of an algebra is a set of elements of the algebra closed under the operations of the algebra.

A subalgebra of higher-dimension loop algebra ˜A2 is constructed, from which a new 3 × 3 isospectral problem is designed.

It follows that k 1 is a subalgebra of maximal rank in so ( 2 d ).

Every BA A can be embedded in a complete BA B in such a way that every element of B is the least upper bound of a set of elements of A. B is unique up to A-isomorphism, and is called the completion of A. If f is a homomorphism from a BA A into a complete BA B, and if A is a subalgebra of C, then f can be extended to a homomorphism of C into B.

We summarize that k 1 has dimension d 2, has rank d, and is a subalgebra of maximal rank in so ( 2 d ).

A basic application of Birkhoff's theorem is in proving the completeness of a proposed axiomatization of a class C. Given an arbitrary model of the axioms, it suffices to show that the model can be constructed as the homomorphic image of a subalgebra of a direct product of algebras of C.

The following two propositions tell us that there is a subalgebra of which does not contain but fails to have the fixed point property.