Original Article
Kyungpook Mathematical Journal 2013; 53(2): 175-184
Published online June 23, 2013
Copyright © Kyungpook Mathematical Journal.
On $BN$-algebras
Chang Bum Kim1,Hee Sik Kim2
1Department of Mathematics, Kookmin University, Seoul, 136-702, Korea
2Department of Mathematics, Hanyang University, Seoul, 133-791, Korea
In this paper, we introduce a $BN$-algebra, and we prove that a $BN$-algebra is $0$-commutative, and an algebra $X$ is a $BN$-algebra if and only if it is a $0$-commutative $BF$-algebra. And we introduce a quotient $BN$-algebra, and we investigate some relations between $BN$-algebras and several algebras.
Keywords: $BN$-algebra, $B$-algebra, $BF$-algebra, Quotient $BN$-algebra, $BN_1$-algebra