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Keywords:
lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice ordered monoid
lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice ordered monoid
Summary:
In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
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