On some generalizations of BCC-algebras

Abstract

We describe weak BCC-algebras (also called BZ-algebras) in which the condition (xy)z=(xz)y is satisfied only in the case when elements x and y belong to the same branch. We also characterize branchwise commutative and branchwise implicative weak BCC-algebras satisfying this condition. We also describe connections between various types of implicative weak BCC-algebras.

Keywords:

• weak BCC-algebra
• BCC-algebra
• branchwise commutative
• branchwise implicative weak BCC-algebra
• BZ-algebra
• branch
• condition (S)

2010 AMS Subject Classifications :

• 03G25
• 06F35