On Differential Semigroups and Radical Differential Ideals

Our objective in this paper is to define a notion of derivation in a semigroup by using its ideals. We call a semigroup with such a derivation, a differential semigroup. ##We study some properties of the derivations in (commutative) semigroups. ##Also we determine the radical differential ideals of any differential monoid by using prime differential ideals