2020/10/17 by Reza Dehghanizade, Dehghanizade, Reza, Seyed Mohamad Sadegh Modarres Mosadegh +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Fuzzy Systems and Optimization #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2010.08724
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.