Ring semigroups whose subsemigroups intersect. (Q734981)

A semigroup is called a ring semigroup if it is the multiplicative semigroup of some ring. For a ring semigroup \((S,\cdot)\) and an addition \(+\) such that \(T=(S,+,\cdot)\) is a ring, it is proved that every two nonzero subsemigroups of \(S\) intersect if and only if \(T\) is either a nil ring or an absolutely algebraic field of prime characteristic \(p\).