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arXiv.org e-Print Archive
Preprint . 2001
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Algebra Universalis
Article . 2002 . Peer-reviewed
License: Springer TDM
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https://dx.doi.org/10.48550/ar...
Article . 2001
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https://dx.doi.org/10.1007/pl0...
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Study of an identity

Study of an identity.
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2002Embargo end date: 01 Jan 2001 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 48, pages 223-248 (issn: 0002-5240, Copyright policy )
Authors: Dehornoy, Patrick;

doi: 10.1007/pl00012451 , 10.48550/arxiv.math/0111158

arXiv: math/0111158

Study of an identity

Abstract

We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity

Related Organizations
Keywords

word problem, Mathematics - Logic, Group Theory (math.GR), 03D40, 08B20, 20N02, Word problems (aspects of algebraic structures), Free algebras, one-generated free algebra, self-distributivity, FOS: Mathematics, Logic (math.LO), Word problems, etc. in computability and recursion theory, Mathematics - Group Theory

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green