Radical of $\cdot$-ideals in $PMV$-algebras

‎In this paper‎, ‎we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$‎. ‎Also‎, ‎we introduce the notion of the radical of a $\cdot$-ideal in $PMV$-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal $\cdot$-ideal in a $PMV$-algebra‎. ‎Finally we show that $A/I$ has no nilpotent elements if and only if $I$ is a semi-maximal $\cdot$-ideal of $A$.