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$DR\ell $-monoid; ideal; prime ideal
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 $A$.
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