Walker's cancellation theorem

Robert Lubarsky; Fred Richman

doi:10.1080/00927872.2012.747598

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arXiv · 1510.02137

Walker's cancellation theorem

Robert Lubarsky·Fred Richman

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Abstract

Walker's cancellation theorem says that if B+Z is isomorphic to C+Z in the category of abelian groups, then B is isomorphic to C. We construct an example in a diagram category of abelian groups where the theorem fails. As a consequence, the original theorem does not have a constructive proof even if B and C are subgroups of the free abelian group on two generators. Both of these results contrast with a group whose endomorphism ring has stable range one, which allows a constructive proof of cancellation and also a proof in any diagram category.

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Robert Lubarsky, Fred Richman. 2015-10-07. Walker's cancellation theorem. https://doi.org/10.1080/00927872.2012.747598

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