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Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive...
Given a poset we introduce the notion of Q-upper algebras and study the (positive) implicativity, commutativity and quasi-commutativity in Q-upper algebras.
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