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Jan Kühr (2005)
Czechoslovak Mathematical Journal
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In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.
Jan Kühr (2006)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this note we describe the structure of dually residuated -monoids (-monoids) that have no non-trivial convex subalgebras.
Jan Kühr (2004)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Lattice-ordered groups, as well as -algebras (pseudo -algebras), are both particular cases of dually residuated lattice-ordered monoids (-monoids for short). In the paper we study ideals of lower-bounded -monoids including -algebras. Especially, we deal with the connections between ideals of a -monoid and ideals of the lattice reduct of .