Let I C R be a proper, prime ideal of R. (a) Let T = RI. Show that T multiplicative set, that is, that 1 ET and if s‚r Є T, then sr ET. We often denote the localization T-¹R by R₁, and call this the "ring R localized at I". (b) Show that m := {iЄI,tЄT} is an ideal of R₁. (c) Show that m is the unique maximal ideal of R. (We say that R, is a local ring in this case, which is just a ring with a unique maximal ideal.)