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Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids. (English) Zbl 1071.06007
Dually residuated lattice-ordered monoids (DR\(\ell \)-monoids, for short) form a wide class of algebras containing, e.g., the classes of lattice-ordered groups, Brouwerian algebras, BL- and pseudo BL-algebras, MV- and GMV-algebras. The author describes connections between ideals of lower-bounded DR\(\ell\)-monoids and ideals of their lattice reducts and studies the sets of idempotent and Boolean elements in those DR\(\ell \)-monoids.

06F05 Ordered semigroups and monoids
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