(One speaks only of residuated algebra for higher arities). A binary (or higher arity) residuated map is usually not residuated as a unary map. If A...

Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation...

residual property The residual function attached to a residuated mapping Residual in a residuated lattice, loosely analogous to division Residue (complex...

adjoint if and only if  f  is a residuated mapping (respectively residual mapping). Therefore, the notion of residuated mapping and monotone Galois connection...

cl(x) ≤ c are equivalent conditions. Every Galois connection (or residuated mapping) gives rise to a closure operator (as is explained in that article)...

\end{alignedat}}} In the language of order theory, the floor function is a residuated mapping, that is, part of a Galois connection: it is the upper adjoint of...

every element x in X. Residual. A dual map attached to a residuated mapping. Residuated mapping. A monotone map for which the preimage of a principal down-set...

Stone. Similarly, the Dedekind–MacNeille completion of a residuated lattice is a complete residuated lattice. However, the completion of a distributive lattice...

The interval [0, 1] equipped with a t-norm and its residuum forms a residuated lattice. The relation between a t-norm T and its residuum R is an instance...

ga(x) = a→x, where → is defined as above. Yet another definition is as a residuated lattice whose monoid operation is ∧. The monoid unit must then be the...