This report discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary non-empty sets. The relationship between such clones and clones in the usual sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. By means of two pairs of kernel and closure operators, a framework is developed that allows to transfer statements about usual clones to statements about clones with nullary constants. In this respect, familiar operators and constructions from clone theory, like the operators Pol and Inv, the closure operators belonging to the clone lattices, and the different variants of local closure operators on sets of relations and operations, respectively, are translated from the usual setting to the more general one and vice versa. The applicability of the presented machinery is demonstrated using the example of the theorem characterising Galois closed sets w.r.t. Pol-Inv as local closures of clones and relational clones, respectively.

This report discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary non-empty sets. The relationship between such clones and clones in the usual sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. By means of two pairs of kernel and closure operators, a framework is developed that allows to transfer statements about usual clones to statements about clones with nullary constants. In this respect, familiar operators and constructions from clone theory, like the operators Pol and Inv, the closure operators belonging to the clone lattices, and the different variants of local closure operators on sets of relations and operations, respectively, are translated from the usual setting to the more general one and vice versa. The applicability of the presented machinery is demonstrated using the example of the theorem characterising Galois closed sets w.r.t. Pol-Inv as local closures of clones and relational clones, respectively.