Direct Sum Cancellation over Noetherian Rings
Suppose X, Y and Z are modules over a commutative ring R and that X⊕Z ≅ Y⊕Z. This cancellation problem is to determine conditions under which one can conclude that X ≅ Y. There are many counterexamples, some interesting, some boring, involving modules that aren’t finitely generated. (For an example of the second sort, take X = 0, Y = R, Z = free module of infinite rank.) In this paper we will assume that all modules are finitely generated. Further, all rings are assumed to be commutative and Noetherian.
KeywordsLocal Ring Maximal Ideal Projective Module Fundamental Unit Jacobson Radical
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