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- W2405399954 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." @default.
- W2405399954 created "2016-06-24" @default.
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- W2405399954 date "2013-01-01" @default.
- W2405399954 modified "2023-09-24" @default.
- W2405399954 title "Walker's Cancellation Theorem." @default.
- W2405399954 hasPublicationYear "2013" @default.
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