GROBNER BASES AND PRIMARY DECOMPOSITION OF MODULES

In this paper I present definitions and algorithms for Gröbner bases for submodules of free modules over polynomial rings in n variables over Noetherian commutative rings with certain algorithmic properties. I then give an algorithm for computing the primary decomposition of submodules of submodules of these free modules when the base ring is also a PID, a show that under certain dimension conditions the requirement of a PID may be dropped. © 1992.