Abstract: Taken Artin ring and semisimple ring as bridges,some localization conditions of SF-ring are constructed for extending the classical characterization of local ring to SF-ring.The properties of groups under the condition of SF-ring localization are further obtained.Finally, the overall dimension of SF-ring localization is discussed.

Key words: SF-ring, localization, semi-simple ring, Artin ring, K₀ group, general dimension