A NOTE ON FULLER’S THEOREM

In 1972, Fuller proved that a complete additive subeategory _RC of R-Mod isequivalent to amodule category ⊿-Mod if and only if _RC=Gen(_RU)for some quasiprogenerator _RU and ⊿≌End _RU canonically. In this note the author gives a characterization of _RC which makes _RU a projective R-module in the case when R is a right perfect ring with identity, and shows that R-Mod is the unique complete additive subcategory of R-Mod which is equivalent to R-Mod for a left Artinian ring R.