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The Extensional Structure of Commutative Noetherian Rings
2003
Communications in Algebra
We show that finitely generated modules over a commutative Noetherian ring can be classified, up to isomorphism of submodule series, in a manner analogous to the classification of integers as products of prime numbers. In outline, two such modules have isomorphic submodule series if and only if 1) the set of minimal associated prime ideals of these modules coincide, 2) the multiplicities of these modules at these prime ideals coincide, and 3) the modules represent the same element in a certain
doi:10.1081/agb-120021881
fatcat:3jv45cpqlreblcmueczii6pbie