Sentence examples for ternary algebra from inspiring English sources

Let  A be a ternary algebra.

Assume that A is a ternary algebra.

Definition 1.4 Let X be a ternary algebra and ( X, N ) be a fuzzy normed space.

We say A has a unit if there exist an element e ∈ A such that [e, e, a] = [eae] = [a, e, e] = a for all a ∈ A. Let A be a ternary algebra and let (A, ǁ.ǁ) be a quasi-Banach space (p-Banach space) (with constant K ≥ 1).

Let A be a linear space over a complex field equipped with a mapping : A3 = A × A × A → A with (x, y, z) ↦ [x, y, z] that is linear in variables x, y, z and satisfies the associative identity [[x, y, z], u, v] = [x, [y, z, u], v] = [x, y, [z, u, v]] for all x, y, z, u, v in A. The pair (A, ) is called a ternary algebra.

Park et al. proved the stability of homomorphisms and derivations in Banach algebras, Banach ternary algebras, C*-algebras, Lie C*-algebras and C*-ternary algebras (see [9 14]).

Then A is called a ternary quasi-Banach algebra (ternary p-Banach algebra) if ǁ[x, y, z] ǁ ≤ K ǁx ǁǁy ǁǁz ǁ for all x, y, z ∈ A. Let A and B be ternary algebras.

Throughout this section, assume that A is a (C^ -ternary algebra with norm (| C^ -ternary

As an application we approximate multi-(C^ -ternary algebra homomorphisms and derivations in these spaC^ -ternary

Therefore, the mapping (f : A rightarrow B) is a multi-(C^ -ternary algebra homomorphism.

Therefore, the mapping (f : A rightarrow B) is a (C^ -ternary algebra homomorphism.