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 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 if there is no infinite strictly ascending chain of principal ideals of the given type (left/right/two-sided) in the ring, or said another way, every ascending chain is eventually constant. The counterpart descending chain condition may also be applied to these posets, however there is currently no need for the terminology "DCCP" since such