Abstract
In this paper, we introduce the notions of γ-homomorphism and γ-derivation of a ternary semigroup and investigate γ-homomorphism and γ-derivations on ternary semigroup associated with the following functional in-equality |f([xyz]) - f(x) - f(y) - f(z)| ≤ φ(x, y, z) and |f([xxx]) - 3f(x)| ≤ φ(x, x, x), respectively.
Highlights
Introduction and preliminariesTernary algebraic operations were considered in the 19th century by several mathematicians such as Cayley [1] who introduced the notion of “cubic matrix” which in turn was generalized by Kapranov, Gelfand and Zelevinskii et al [2]
We introduce the notions of g-homomorphism and g-derivation of a ternary semigroup and investigate g-homomorphism and g-derivations on ternary semigroup associated with the following functional in-equality |f([xyz]) - f(x) - f(y) - f (z)| ≤ (x, y, z) and |f([xxx]) - 3f(x)| ≤ (x, x, x), respectively. 2000 MSC: Primary 39B52, Secondary 39B82; 46B99; 17A40
1 Introduction and preliminaries Ternary algebraic operations were considered in the 19th century by several mathematicians such as Cayley [1] who introduced the notion of “cubic matrix” which in turn was generalized by Kapranov, Gelfand and Zelevinskii et al [2]
Summary
Introduction and preliminariesTernary algebraic operations were considered in the 19th century by several mathematicians such as Cayley [1] who introduced the notion of “cubic matrix” which in turn was generalized by Kapranov, Gelfand and Zelevinskii et al [2]. A mapping f : (G, [ ]) ® (G, [ ]) is called a ternary homomorphism if f ([xyz]) = [f (x)f (y)f (z)]
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