Uig, Skye north and the River Conon which drains Glen Uig to the east. The lower courses of both of these small rivers are characterised by waterfalls. Uigg, Prince Edward Island, Canada was named by settlers from Uig. The population is estimated to be between 200–300 inhabitants. Uig is served by the A87 road from Portree and Kyle of Lochalsh to the south and the A855 road which runs northwards around the end of the Trotternish peninsula before also turning south to Portree. As of August, 2006, Uig is accessible via intercity buses on Skye, and Scottish Citylink buses, which travel as
Principal ideal principal ideals in formula_43 are of the form formula_44. Actually, every ideal formula_1 in formula_43 is principal, which can be shown in the following way. Suppose formula_47 where formula_48, then consider the surjective homomorphisms formula_49 Since formula_50 is finite, then for sufficiently large formula_51, formula_52 Thus, formula_53, which implies formula_1 is always finitely generated. Since the ideal generated by any integers formula_3 and formula_56, formula_57, is exactly formula_58, by induction on the number of generators, it follows that formula_1 is principal. However, all rings have principal ideals, namely, any ideal generated by exactly one element. For example, the ideal formula_60