Über das Radikal in potenzverbundenen Halbgruppen
For a semigroup S define an equivalence rad S: (a,b)\(\in rad S\) iff for every \(s\in S\) there exist i,j,k,m with \((as)^ ia=(as)^ jb\) and \((bs)^ ka=(bs)^ mb.\) Let S be a semigroup such that for every pair a,\(b\in S\) there exist m, n with \(a^ m=b^ n\). The paper investigates the equivalence rad S on S. As typical results of this paper we give: rad S is a congruence and it is identical iff S is cancellative. The following conditions on S are equivalent: a) S is right cancellative, b) S is left cancellative, c) S is cancellative, d) S is right separative, e) S is left separative, f) S is separative.
scientific article; zbMATH DE number 3859413