Portree High School Portree High School Portree High School (Gaelic: ) is a state co-educational comprehensive school in Portree, Skye in Scotland. , the school enrols 520 pupils and employs 55 teachers. The school's catchment area draws from 15 primary schools across Skye and neighbouring Raasay. The school also has boarding provisions for a small number of pupils who live in more remote areas of the island. A school has existed at Portree since the 17th century. However it closed in 1825 due to the difficulty in finding a new qualified schoolmaster. Construction on the Portree High School buildings began in 1872. In
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