Semigroups in which the radical of every ideal is a subsemigroup
Stojan Bogdanović, Miroslav Ćirić
In this paper we consider semigroups $S$ in which $\sqrt A=\{x\in S\mid(\exists n\in\mathbf Z^+)x^n\in A\}$ is a subsemigroup of $S$ for every ideal $A$ of $S$.