On algebras with a generalized implication

Year, pages: 2013, 947 - 958

We introduce the notion of $gi$-algebra as a generalization of dual $BCK$-algebra, and define the notions of strong, commutative and transitive $gi$-algebra, and then we show that an interval $\ua l=\{a\in P \mid l≤ a\}$ in a strong and commutative $gi$-algebra $P$ is a lattice. Also, we define a congruence relation $\sim_D$ on a transitive $gi$-algebra $P$ and show that the quotient set $P/{\sim_D}$ is a $gi$-algebra and a dual $BCK$-algebra.

Yon, Y., Kim, K. 2013. On algebras with a generalized implication. In Mathematica Slovaca, vol. 63, no.5, pp. 947-958. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0146-x

Yon, Y., Kim, K. (2013). On algebras with a generalized implication. Mathematica Slovaca, 63(5), 947-958. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0146-x