Abstract. In this paper we introduce the notion of BG-algebras which is a generalization of .B-algebras. We construct a BG-algebra from a non-empty set, which is non-group-derived. Moreover, using the notion of normal subalgebra, we obtain several isomorphism theorems of BG-algebra and related properties. BCH/BCI/BCKalgebras, i.e., (I); (II) and (IV) x * y = 0 and y * x = 0 imply x = y, for any x,y € X. In this paper we introduce the notion of 5G-algebras which is a generalization of .B-algebras. We construct a .BG-algebra from a non-empty set, which is non-group-derived. Moreover, using the notion of normal subalgebra, we obtain several isomorphism theorems of .BG-algebra and related properties.1991 Mathematics Subject Classification: 06F35.
Abstract. 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.
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