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- W2987287312 abstract "A residuated lattice is defined to be integrally closed if it satisfies the equations xx = e and x/x = e. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral. It is proved that the mapping a -> (ae)e on any integrally closed residuated lattice is a homomorphism onto a lattice-ordered group. A Glivenko-style property is then established for varieties of integrally closed residuated lattices with respect to varieties of lattice-ordered groups, showing in particular that integrally closed residuated lattices form the largest variety of residuated lattices admitting this property with respect to lattice-ordered groups. The Glivenko property is used to obtain a sequent calculus admitting cut-elimination for the variety of integrally closed residuated lattices and to establish the decidability, indeed PSPACE-completenes, of its equational theory. Finally, these results are related to previous work on (pseudo) BCI-algebras, semi-integral residuated partially ordered monoids, and algebras for Casari's comparative logic." @default.
- W2987287312 created "2019-11-22" @default.
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- W2987287312 date "2019-02-21" @default.
- W2987287312 modified "2023-09-27" @default.
- W2987287312 title "Integrally Closed Residuated Lattices." @default.
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