Geodesic
Lexicographic extensions of dually residuated lattice ordered monoids
Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 283-295

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MR Zbl
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 $-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
Dually residuated lattice ordered monoids ($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.
DOI : 10.21136/MB.2004.134151
Classification : 03G10, 03G25, 06D35, 06F05, 06F15
Keywords: $DR\ell $-monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics 
Rachůnek, Jiří; Šalounová, Dana. Lexicographic extensions of dually residuated lattice ordered monoids. Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 283-295. doi: 10.21136/MB.2004.134151
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