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 principal ideals in formula_43 are of the form formula_44. Actually, every ideal formula_1 in formula_43 is principal, which can be shown in the following way. Suppose formula_47 where formula_48, then consider the surjective homomorphisms formula_49 Since formula_50 is finite, then for sufficiently large formula_51, formula_52 Thus, formula_53, which implies formula_1 is always finitely generated. Since the ideal generated by any integers formula_3 and formula_56, formula_57, is exactly formula_58, by induction on the number of generators, it follows that formula_1 is principal. However, all rings have principal ideals, namely, any ideal generated by exactly one element. For example, the ideal formula_60