Šlapal, Josef Direct arithmetics of relational systems. (English) Zbl 0733.08001 Publ. Math. Debr. 38, No. 1-2, 39-48 (1991). The paper deals with relational systems of arbitrary arity, i.e. with systems \({\mathbb{G}}=(G,R)\) where G is a set (the carrier of \({\mathbb{G}})\), I is a given set (the domain of \({\mathbb{G}})\) and \(R\subseteq G^ I\) is a set of mappings from I into G (the relation of \({\mathbb{G}})\). For relational systems with the same domain, the direct operations of sum, product and power are defined and expected properties of these operations are proved. Especially, for the power, a sufficient condition for the validity of the rule \((({\mathbb{G}})^{{\mathbb{H}}})^{{\mathbb{K}}}\sim {\mathbb{G}}^{{\mathbb{H}}\cdot {\mathbb{K}}}\) is given. Reviewer: V.Novak (Brno) Cited in 1 ReviewCited in 5 Documents MSC: 08A02 Relational systems, laws of composition Keywords:reflexive system; diagonal system; relational systems; sum; product; power PDFBibTeX XMLCite \textit{J. Šlapal}, Publ. Math. Debr. 38, No. 1--2, 39--48 (1991; Zbl 0733.08001)