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PROBLEM TO BE SOLVED : To provide an oxide sol or hydroxide sol of a rare earth element having less univalent inorganic acid radicals and excellent in stability as the sol. SOLUTION : This oxide sol or hydroxide sol of the rare earth element M has a median size of 10-300 nm, and contains hydroxycarboxylic acid within the range of 0.05-0.5 in the mole ratio of hydroxycarboxylic acid/M2O3(wherein M is a rare earth element selected from Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu). Since such a sol does not substantially contain univalent inorganic acid radicals or is extremely few in amount even if contained, there is no generation of unnecessary gas during sintering and no adverse effect on a furnace casing or environment. Further, the sol is enormously stable to be extremely effective for performance gain of the products using rare earth elements. COPYRIGHT : (C)2006, JPO&NCIPI