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 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