A simple proof of Vinogradov's theorem on the orderability of the free product of $o$-groups

Révész, Gábor

doi:10.21136/cmj.1987.102156

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2018

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“…A proof given in [4] was unfortunately found to have a gap, as discussed in [7] and [6]. Yet another proof, in [14], was also shown to have a gap [12].…”

Section: Introductionmentioning

confidence: 99%

Ordered groups as a tensor category

Rolfsen

2018

Pacific J. Math.

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It is a classical theorem that the free product of ordered groups is orderable. In this note we show that, using a method of G. Bergman, an ordering of the free product can be constructed in a functorial manner, in the category of ordered groups and order-preserving homomorphisms. With this functor interpreted as a tensor product this category becomes a tensor (or monoidal) category. Moreover, if O(G) denotes the space of orderings of the group G with the natural topology, then for fixed groups F and G our construction can be considered a function O(F ) × O(G) → O(F * G). We show that this function is continuous and injective. Similar results hold for left-ordered groups.

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“…A proof given in [4] was unfortunately found to have a gap, as discussed in [7] and [6]. Yet another proof, in [14], was also shown to have a gap [12].…”

Section: Introductionmentioning

confidence: 99%

Ordered groups as a tensor category

Rolfsen

2018

Pacific J. Math.

View full text Add to dashboard Cite

show abstract

A simple proof of Vinogradov's theorem on the orderability of the free product of $o$-groups

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Cited by 1 publication

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Ordered groups as a tensor category

Ordered groups as a tensor category

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