Radical of ⋅-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 ⋅-ideal in PMV-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal ⋅-ideal in a PMV-algebra‎. ‎Finally we show that A/I has no nilpotent elements if and only if I is a semi-maximal ⋅-ideal of A.