On BV-Algebras - In Ho Hwang; Yong Lin Liu; Hee Sik Kim (Mathematics, 2020)
In this paper, we introduce the notion of a <semantics>BV</semantics>-algebra, and we show that a <semantics>BV</semantics>-algebra is logically equivalent to several algebras, i.e., <semantics>BM</semantics>-algebras, <semantics>BT</semantics>-algebras, <semantics>BO</semantics>-algebras and 0-commutative B-algebras. Moreover, we show that a <semantics>BV</semantics>-algebra with <semantics>(F)</semantics> is logically equivalent to several algebras, and we show some relationships between a <semantics>BV</semantics>-algebra with <semantics>(F)</semantics> and several related algebras.