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Inverse topology in MV-algebras

Fereshteh Forouzesh, Farhad Sajadian, Mahta Bedrood (2019)

Mathematica Bohemica

We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra A and show that the set of all minimal prime ideals of A , namely Min ( A ) , with the inverse topology is a compact space, Hausdorff, T 0 -space and T 1 -space. Furthermore, we prove that the spectral topology on Min ( A ) is a zero-dimensional Hausdorff topology and show that the spectral topology on Min ( A ) is finer than the inverse topology on Min ( A ) . Finally, by open sets of the inverse topology, we define and study a congruence relation...

Join-semilattices whose sections are residuated po-monoids

Ivan Chajda, Jan Kühr (2008)

Czechoslovak Mathematical Journal

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 sectionally residuated semilattice. 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...

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