$\beta$-algebras and related topics

Young Hee Kim; Keum Sook So

doi:10.4134/CKMS.2012.27.2.217

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Commun. Korean Math. Soc. 2012; 27(2): 217-222

Printed June 1, 2012

https://doi.org/10.4134/CKMS.2012.27.2.217

$\beta$-algebras and related topics

Young Hee Kim and Keum Sook So

Chungbuk National University, Hallym University

Abstract

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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

MSC numbers: 06F35