Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(2): 281-287

Printed March 1, 2009

https://doi.org/10.4134/BKMS.2009.46.2.281

Copyright © The Korean Mathematical Society.

On generalized upper sets in $BE$-algebras

Sun Shin Ahn and Keum Sook So

Dongguk University and Hallym University

Abstract

In this paper, we develop the idea of a generalized upper set in a $BE$-algebra. Furthermore, these sets are considered in the context of transitive and self distributive $BE$-algebras and their ideals, providing characterizations of one type, the generalized upper sets, in terms of the other type, ideals.

Keywords: $BE$-algebra, ideal, (generalized) upper set, self distributive

MSC numbers: 06F35