Quasi-algebra, a special sample of quasilinear spaces

Abstract: Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce quasi-algebras and normed quasi-algebras with the help of what was done in constructing algebras. After examining some properties of these new spaces, we introduce the concept of quasi-homomorphisms that is an instance of a quasilinear operator. Moreover since the study of spaces with algebraic structures cannot be completed without the study of spectrums, we define the concept of quasi-spectrum on quasi-algebras as we expect it to be.