The smallest ideals of \(\beta\mathbb N\) under addition and multiplication (Q1779248)

The author gives a proof of the following very interesting result: It has been known for some time that the smallest ideals of \((\beta\mathbb{N},+)\) and \((\beta\mathbb{N},\cdot)\) are disjoint and that the closure of the former meets the latter. It is shown here that the closure of the smallest ideal of \((\beta\mathbb{N},\cdot)\) misses the smallest ideal of \((\beta\mathbb{N},+)\). Indeed, a stronger statement holds: it misses \(\mathbb{N}^*+ \mathbb{N}^*\).