Flat embeddings of noetherian algebras in artinian rings

Abstract

It is shown that a noetherian algebraR with finite Gelfand-Kirillov dimension and right primary decomposition can be embedded in an artinian ringS, and thatS is flat as a leftR-module if and only if all right associated primes are minimal. IfR is irreducible then such a flat embedding is possible if and only ifR has an artinian quotient ring. Also, the existence of a left flat embedding in an artinian ring allows an explicit description of the prime middle annihilators ofR.