Some Implicativities for Groupoids and <i>BCK</i>-Algebras

• Main Authors: In Ho Hwang, Hee Sik Kim, Joseph Neggers
• Format: Article
• Language: English
• Published: MDPI AG 2019-10-01
• Series: Mathematics
• Subjects: groupoid; <i>d</i>-algebra; <i>bck</i>-algebra; (weakly) (<i>i</i>-)implicative; condition (<i>l_i</i>)
• Online Access: https://www.mdpi.com/2227-7390/7/10/973
• ISSN: 2227-7390

In this paper, we generalize the notion of an implicativity discussed in <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mi>C</mi> <mi>K</mi> </mrow> </semantics> </math> </inline-formula>-algebras, and apply it to some groupoids and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mi>C</mi> <mi>K</mi> </mrow> </semantics> </math> </inline-formula>-algebras. We obtain some relations among those axioms in the theory of groupoids.