Walker's Cancellation Theorem

3 pages•Published: July 28, 2014

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. In fact, in our example B and C are subgroups of
Z<sup>2</sup>. 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.

Keyphrases: abelian groups, constructivism, diagram category, kripke model

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 145-147.

Links:	https://easychair.org/publications/paper/mk2c
	https://doi.org/10.29007/vz4n

BibTeX entry

@inproceedings{TACL2013:Walkers_Cancellation_Theorem,
  author    = {Robert Lubarsky and Fred Richman},
  title     = {Walker's Cancellation Theorem},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/mk2c},
  doi       = {10.29007/vz4n},
  pages     = {145-147},
  year      = {2014}}

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