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
Principal ideal is a principal ideal of formula_61, and formula_62 is a principal ideal of formula_63. In fact, formula_64 and formula_65 are principal ideals of any ring formula_2. A ring in which every ideal is principal is called "principal", or a principal ideal ring. A principal ideal domain (PID) is an integral domain in which every ideal is principal. Any PID must be a unique factorization domain; the normal proof of unique factorization in the integers (the so-called fundamental theorem of arithmetic) holds in any PID. Any Euclidean domain is a PID; the algorithm used to calculate greatest common divisors may be