Locally perfect commutative rings are those whose modules have maximal submodules

R denotes a commutative ring. After BassB], a ring R is perfect in case every module has a projective cover. A ring R is a max ring provided that every nonzero i2-module has a maximal submodule. Bass characterized perfect rings as semilocal rings with T-nilpotent Jacobson radical J, and showed they are max rings. Moreover, Bass proved that R is perfect iff R satisfies the dec on principal ideals. Using Bass' theorems, the Hamsher-Koifman (H],K]) characterization of max R (see (3) ?(4) below), and the characterization of max R by the author via subdirectly irreducible quasi-injective R-modules, we obtain.