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
Ascending chain condition on principal ideals it satisfies the right ACCP. The converses are not true, and the above switches from "left" and "right" are not typos. Whether the ACCP holds on the right or left side of "R", it implies that "R" has no infinite set of nonzero orthogonal idempotents, and that "R" is a Dedekind finite ring. Ascending chain condition on principal ideals In abstract algebra, the ascending chain condition can be applied to the posets of principal left, principal right, or principal two-sided ideals of a ring, partially ordered by inclusion. The ascending chain condition on principal ideals (abbreviated to ACCP) is satisfied