sentences:  Let "B" be the localization of "R" with respect to all elements not in either "m" or "n".Then "B" is a 2-dimensional Noetherian semi-local ring with 2 maximal ideals, "mB" (of height 1) and "nB" (of height 2).Let "I" be the Jacobson radical of "B", and let "A" = "k"+"I".