25 citations · 39 across the 40 of their papers we have counts for
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Residuated operators and Dedekind-MacNeille completion
Ivan Chajda, Helmut Länger, Jan Paseka
The concept of operator residuation for bounded posets with unary operation was introduced by the first two authors. It turns out that in some cases when these operators are transf…
Residuation in modular lattices and posets
Ivan Chajda, Helmut Länger
We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The…
Orthomodular lattices can be converted into left residuated l-groupoids
Ivan Chajda, Helmut Länger
We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional condi…
Residuated operators in complemented posets
Ivan Chajda, Helmut Länger
Using the operators of taking upper and lower cones in a poset with a unary operation, we define operators M(x,y) and R(x,y) in the sense of multiplication and residuation, respect…
When does a semiring become a residuated lattice?
Ivan Chajda, Helmut Länger
It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied triviall…