Idempotent residuated structures : some category equivalences and their applications

Show simple item record Galatos, N. Raftery, James G. 2015-03-05T08:50:39Z 2015-03-05T08:50:39Z 2015
dc.description.abstract This paper concerns residuated lattice-ordered idempotent commutative monoids that are subdirect products of chains. An algebra of this kind is a generalized Sugihara monoid (GSM) if it is generated by the lower bounds of the monoid identity; it is a Sugihara monoid if it has a compatible involution :. Our main theorem establishes a category equivalence between GSMs and relative Stone algebras with a nucleus (i.e., a closure operator preserving the lattice operations). An analogous result is obtained for Sugihara monoids. Among other applications, it is shown that Sugihara monoids are strongly amalgamable, and that the relevance logic RMt has the projective Beth de nability property for deduction. en_ZA
dc.description.librarian hb2015 en_ZA
dc.description.uri en_ZA
dc.identifier.citation Galatos, N & Raftery, JG 2015, 'Idempotent residuated structures : some category equivalences and their applications',Transactions of the American Mathematical Society, vol. 367, no. 5, pp. 3189-3223. en_ZA
dc.identifier.issn 0002-9947 (print)
dc.identifier.issn 1088-6850 (online)
dc.language.iso en en_ZA
dc.publisher American Mathematical Society en_ZA
dc.rights First published in Transactions of the American Mathematical Society in vol 36, no. 4. 2015, published by the American Mathematical Society. en_ZA
dc.subject Idempotent en_ZA
dc.subject Residuation en_ZA
dc.subject Semilinear en_ZA
dc.subject Representable en_ZA
dc.subject Nucleus en_ZA
dc.subject Sugihara monoid en_ZA
dc.subject Relative Stone algebra en_ZA
dc.subject Category equivalence en_ZA
dc.subject Epimorphism en_ZA
dc.subject Amalgamation en_ZA
dc.subject Beth de nability en_ZA
dc.subject Interpolation en_ZA
dc.subject R-mingle en_ZA
dc.title Idempotent residuated structures : some category equivalences and their applications en_ZA
dc.type Article en_ZA

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