On some generalizations of BCC-algebras
Wieslaw A.Dudek, Janus Thomys

TL;DR
This paper introduces and characterizes weak BCC-algebras, exploring their properties when a specific associativity condition holds within branches, and examines relationships among different implicative variants.
Contribution
It defines weak BCC-algebras with branch-specific associativity and characterizes branchwise commutative and implicative cases, expanding the understanding of BCC-algebra generalizations.
Findings
Weak BCC-algebras satisfy (xy)z=(xz)y only within the same branch.
Characterization of branchwise commutative weak BCC-algebras.
Connections between various implicative weak BCC-algebra types.
Abstract
We describe weak BCC-algebras (also called BZ-algebras) in which the condition is satisfied only in the case when elements 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.
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