Composition on FL_<i>ew</i>-algebras

Abstract We introduce the notion of CFL ew -algebras, which are bounded commutative integral residuated lattices equipped with an additional operation that mimics the composition of functions. We obtain and study some of the basic properties of CFL ew -algebras. In particular, we characterize semi-divisible CFL ew -algebras and prove that Boolean algebras are the only CFL ew -algebras having sub-CFL ew -algebras of order 4. Finally, we study the effect of the composition on the filters/congruences of CFL ew -algebras and also investigate the usual constructions of subalgebras, quotient algebras, as well as related classes of filters.