Young Hee Kim and Keum Sook So Chungbuk National University, Hallym University
Abstract : In this note we investigate some properties of $\beta$-algebras and further relations with $B$-algebras. Especially, we show that if $(X,-,+,0)$ is a $B^*$-algebra, then $(X,+)$ is a semigroup with identity 0. We discuss some constructions of linear $\beta$-algebras in a field $K$.
Keywords : $\beta$-algebra, $B$-algebra, $B^*$-algebra, linear