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Spectral topologies of dually residuated lattice-ordered monoids. (English) Zbl 1080.06023
Summary: Dually residuated lattice-ordered monoids ($$DR\ell$$-monoids for short) generalize lattice-ordered groups and include for instance also GMV-algebras (pseudo MV-algebras), a non-commutative extension of MV-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
##### MSC:
 06F05 Ordered semigroups and monoids 06D35 MV-algebras
##### Keywords:
$$DR\ell$$-monoid; prime ideal; spectrum
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