Geodesic
On idempotent elements of dually residuated lattice ordered semigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 479-483.

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We show that idempotent elements of a dually residuated lattice ordered semigroup (a DRl-semigroup) form a Brouwerian algebra. Further we show that for any idempotent elements x,y such that x≤ y the interval [x;y] is also a DRL-semigroup.
Keywords: BL-algebra, Boolean algebra, Brouwerian algebra, lattice ordered group, lattice ordered monoid, MV-algebra, dually residuated lattice ordered semigroup 
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Kovář, Tomáš. On idempotent elements of dually residuated lattice ordered semigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 479-483. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a14/

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[3] K.L.N. Swamy, Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965) 105–114. https://doi.org/10.1007/BF01360284