\((3,3)\)-ary differential rings.
A \((3,3)\)-ary differential ring is a system \((R,f,g,\Delta)\) where \(R\) is a nonempty set, \(f\) and \(g\) are ternary compositions such that \((R,f)\) is a ternary Abelian group with a neutral element, \(g\) is associative and tridistributive with respect to \(f\), \(\Delta\) is a set of derivations such that for each derivation \(d\) and every \(x,y,z\) in \(R\), \(d(f(x,y,z))=f(d(x),d(y),d(z))\) and \(d(g(x,y,z))=f(g(d(x),y,z),g(x,d(y),z),g(x,y,d(z))\). The authors introduce and study some concepts as ideals of \(R\), semiprime and prime ideals, radicals, nilradical. In the last section, applications to hypergroups and ternary hypergroups with orderings, and to automata are given.
scientific article; zbMATH DE number 6107815
scientific article