Inverness-shire Inverness-shire is Scotland's largest county, and the second largest in the UK as a whole after Yorkshire. It borders Ross to the north, Nairnshire, Moray, Banffshire and Aberdeenshire to the east, and Perthshire and Argyll to the south. It covers a large mainland area and various island areas off the west coast. The mainland area has coastline in both the east and the west. The island areas include North Uist, South Uist and Harris in the Outer Hebrides and Skye and the Small Isles in the Inner Hebrides. Principal settlements include Inverness, Fort William, Fort Augustus and Portree. Inverness-shire's coat
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