Abstract
In this paper, we introduce the notion of a BV-algebra, and we show that a BV-algebra is logically equivalent to several algebras, i.e., BM-algebras, BT-algebras, BO-algebras and 0-commutative B-algebras. Moreover, we show that a BV-algebra with (F) is logically equivalent to several algebras, and we show some relationships between a BV-algebra with (F) and several related algebras.
Highlights
The notion of BCK-algebras was formulated by Iséki
We show that a BV-algebra with ( F ) is logically equivalent to several algebras, and we show some relationships between a BV-algebra with ( F ) and several related algebras
We introduced the notion of a BV-algebra, and investigated some relations between BV-algebras and their related topics
Summary
The notion of BCK-algebras was formulated by Iséki. Jun et al [5] introduced the notion of a BH-algebra, which is a generalization of BCK/BCI/B-algebras. Kim and Kim [7] defined the notion of a BM-algebra They showed that a BM-algebra is equivalent to a 0-commutative B-algebra. Introduced the notion of a BO-algebra, and proved that every BO-algebra is 0-commutative, and obtained several algebras which are logically equivalent to the BO-algebra. Kim and Kim [10] defined the notion of a BN-algebra, and showed that an algebra A is a BN-algebra if and only if it is a 0-commutative BF-algebra. We introduce the notion of a BV-algebra consisting of 3 simple axioms, and we show it is logically equivalent to several known algebras. We show that a BV-algebra with ( F ) is logically equivalent to several algebras, and we show some relationships between a BV-algebra with ( F ) and several related algebras
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