On BV-Algebras

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.

Hyperstructure Theory Applied to BF-Algebras

“…They also presented the concept of BN-algebra [6] and provided some equivalent conditions related to BN-algebra. Hwang et al defined BV-algebra and showed that it is logically equivalent to BT-algebra, BM-algebra, 0-commutative B-algebra, and BV-algebra in [7]. The term BP-algebra was created by Ahn and Han [8], who also demonstrated that the quadratic BP-algebra is identical to multiple quadratic algebras.…”

Fuzzy Product KM‐Subalgebras and Some Related Properties

“…Ansari et al [1,2], Hong et al [3], Qing-ping Hu [4], and Hwang et al [5] researched a new class of algebra called BCH-algebras and analyzed that the class of BCI-algebras is a proper subclass of BCH-algebras. BCK-algebra was first introduced in 1966, thanks to the mathematicians Imai and Iséki [6] and has since been used in a variety of fields in mathematics, such as Topology, Probability theory, Functional Analysis, and Group theory.…”