Abstract :
LetA,B, andCbe modules over a unital ringRsuch thatCis Noetherian andA circled plus C congruent with B circled plus C. Even thoughAandBneed not be isomorphic, we show that they have isomorphic submodule series, and, equivalently, thatAandBare indistinguishable by functions on the category ofR-modules that respect short exact sequences.
