Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations

3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015

数学;化学;物理学

Ehsani, Amir^1

Department of Mathematics, Mahshshar Branch, Islamic Azad University, Mahshahr, Iran^1

关键词: Abelian group;    Binary operations;    Functional equation;    Linear representation;    Quadratic functional equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/622/1/012037/pdf
DOI  :  10.1088/1742-6596/622/1/012037

来源: IOP

【 摘 要 】

Algebras with a pair of non-associative binary operations (f, g) which are satisfy in the balanced quadratic functional equations with four object variables considered. First, we obtain a linear representation for the operations, of this kind of binary algebras (A,f,g), over an abelian group (A, +) and then we generalize the linear representation of operations, to an algebra (A,F) with non-associative binary operations which are satisfy in the balanced quadratic functional equations with four object variables.