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dc.contributor.authorElston, G.Z.
dc.contributor.authorNehaniv, C.L.
dc.identifier.citationElston , G Z & Nehaniv , C L 2002 , ' Holonomy Embedding for Arbitrary Stable Semigroups ' , International Journal of Algebra and Computation , vol. 12 , no. 6 , pp. 791-810 .
dc.identifier.otherPURE: 97493
dc.identifier.otherPURE UUID: 4d732c1f-c8ed-4c4a-8f4d-b0f78d1c7621
dc.identifier.otherdspace: 2299/4304
dc.identifier.otherScopus: 0036996699
dc.descriptionOriginal article can be found at: Copyright World Scientific Publishing Company. DOI: 10.1142/S0218196702001206 [Full text of this article is not available in the UHRA]
dc.description.abstractWe show how the Rhodes expansion Ŝ of any stable semigroup S embeds into the cascade integral (a natural generalization of the wreath product) of permutation-reset transformation semigroups with zero adjoined. The permutation groups involved are exactly the Schützenberger groups of the -classes of S. Since S ←← Ŝ is an aperiodic map via which all subgroups of S lift to Ŝ, this results in a strong Krohn–Rhodes–Zeiger decomposition for the entire class of stable semigroups. This class includes all semigroups that are finite, torsion, finite -above, compact Hausdorff, or relatively free profinite, as well as many other semigroups. Even if S is not stable, one can expand it using Henckell's expansion and then apply our embedding. This gives a simplified proof of the Holonomy Embedding theorem for all semigroups.en
dc.relation.ispartofInternational Journal of Algebra and Computation
dc.titleHolonomy Embedding for Arbitrary Stable Semigroupsen
dc.contributor.institutionSchool of Computer Science
dc.contributor.institutionScience & Technology Research Institute
dc.description.statusPeer reviewed
rioxxterms.typeJournal Article/Review

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