Geodesic
Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 105-112

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Lattice-ordered groups, as well as $GMV$-algebras (pseudo $MV$-algebras), are both particular cases of dually residuated lattice-ordered monoids ($DR\ell $-monoids for short). In the paper we study ideals of lower-bounded $DR\ell $-monoids including $GMV$-algebras. Especially, we deal with the connections between ideals of a $DR\ell $-monoid $A$ and ideals of the lattice reduct of $A$.
Classification : 03G25, 06F05
Keywords: $DR\ell $-monoid; ideal; prime ideal 
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Kühr, Jan. Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 105-112. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a9/