




Volume 34 • Number 3 • 2011 

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Extended Upper Sets in $BE$Algebras
Hee Sik Kim and Kyoung Ja Lee
Abstract.
As a generalization of a $BCK$algebra, a $BE$algebras was introduced. In this paper, we investigate several properties of upper sets in $BE$algebras, and we introduce more extended upper sets of $BE$algebras, and obtain some relations with filters of $BE$algebras. Also, the notion of Krull dimension of a $BE$algebra and the notion of regular sequence in a $BE$algebra are introduced.
2010 Mathematics Subject Classification: 03G25, 06B10, 06E10.
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