Portree Portree Portree (; , ) is the largest town on Skye in the Inner Hebrides of Scotland. It is the location for the only secondary school on the island, Portree High School. Public transport services are limited to buses. Portree has a harbour, fringed by cliffs, with a pier designed by Thomas Telford. Attractions in the town include the Aros centre which celebrates the island's Gaelic heritage. Further arts provision is made through arts organisation ATLAS Arts, a Creative Scotland regularly-funded organisation. The town also serves as a centre for tourists exploring the island. The Royal Hotel is the site
Principal ideal ring Left Bézout rings are defined similarly. These conditions are studied in domains as Bézout domains. A commutative principal ideal ring which is also an integral domain is said to be a "principal ideal domain" (PID). In this article the focus is on the more general concept of a principal ideal ring which is not necessarily a domain. If "R" is a right principal ideal ring, then it is certainly a right Noetherian ring, since every right ideal is finitely generated. It is also a right Bézout ring since all finitely generated right ideals are principal. Indeed, it is clear that