In 1975, Cresp and Sullivan described all rings which satisfy certain conditions on their multiplicative structure: in particular, those rings
for which every multiplicative endomorphism is an additive endomorphism. In 1977, Sullivan proposed an alternative problem: describe
all rings for which every additive endomorphism is a multiplicative endomorphism, and later several authors referred to this as 'Sullivan's Problem'. In this talk, we discuss some attempts to solve this problem using abelian group theory, and we suggest there may be a better approach via semigroup theory (as originally intended).