Abstract
Most mathematical notions have connections with real life. Although the theory of rings and algebras is abstract, however, this theory has many applications, some indirect, in real life. Many sets of real-life objects, taken together with one or more laws of composition, form algebraic structures with interesting properties. Quaternion algebras and of symbol algebras have applications in various branches of mathematics, but also in computer science, physics, signal theory. In this paper we define and we study properties of \(\left( l,1,p+2q,q\cdot l\right) -\) numbers, \(\left( l,1,p+2q,q\cdot l\right) -\) quaternions, \(\left( l,1,p+2q,q\cdot l\right) -\) symbol elements. Finally, we obtain an algebraic structure with these elements.
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