On some generalizations of BCC-algebras
classification
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keywords
bcc-algebrasweakbranchwiseconditiondescribeimplicativebelongbranch
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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 $x,y$ 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.
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