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Keywords:
$DR\ell $-monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics
Summary:
Dually residuated lattice ordered monoids ($DR\ell $-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ($MV$-algebras, $BL$-algebras) and their non-commutative variants ($GMV$-algebras, pseudo $BL$-algebras). In the paper, lex-extensions and lex-ideals of $DR\ell $-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
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