Volume 34 • Number 3 • 2011   • 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. Full text: PDF