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Finite-valued dually residuated lattice-ordered monoids. (English) Zbl 1141.06014
Summary: Lattice-ordered groups, as well as $$\roman {GMV}$$-algebras (called also pseudo $$\roman {MV}$$-algebras), are both particular cases of dually residuated lattice-ordered monoids ($$\roman {DR}\ell$$-monoids). In the paper we study values in $$\roman {DR}\ell$$-monoids, especially if the ideal lattice is a member of the class $$\mathcal {TRN}$$ of algebraic, distributive lattices whose compact elements form a relatively normal sublattice, and we characterize finite-valued $$\roman {DR}\ell$$-monoids whose ideal lattices belong to $$\mathcal {TRN}$$.

##### MSC:
 06F05 Ordered semigroups and monoids 06D35 MV-algebras 03G25 Other algebras related to logic
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##### References:
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