Displaying similar documents to “Pseudocomplemented directoids”

Ring-like structures derived from λ -lattices with antitone involutions

Ivan Chajda (2007)

Mathematica Bohemica

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Using the concept of the λ -lattice introduced recently by V. Snášel we define λ -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

Join-semilattices whose sections are residuated po-monoids

Ivan Chajda, Jan Kühr (2008)

Czechoslovak Mathematical Journal

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We generalize the concept of an integral residuated lattice to join-semilattices with an upper bound where every principal order-filter (section) is a residuated semilattice; such a structure is called a . Natural examples come from propositional logic. For instance, implication algebras (also known as Tarski algebras), which are the algebraic models of the implication fragment of the classical logic, are sectionally residuated semilattices such that every section is even a Boolean algebra....