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Antivarieties of unars

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Algebra and Logic Aims and scope

A complete description of the lattice of all antivarieties of unars is given. It is stated that there exist continuum many antivarieties of unars not having an independent basis of anti-identities and a necessary and sufficient condition is specified under which a finite unar has an independent or finite basis of anti-identities. In addition, it is proved that the lattice of all antivarieties of unars is isomorphic to a lattice of \( {{\mathcal A}_{1,1}} \)-antivarieties, where \( {{\mathcal A}_{1,1}} \) is a variety of unary algebras of a signature < f, g > defined by identities f(g(x)) = g(f(x)) = x.

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Authors and Affiliations

  1. P/B 1542, Volgograd, 400120, Russia

    A. V. Kartashova

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  1. A. V. Kartashova
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Correspondence to A. V. Kartashova.

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Translated from Algebra i Logika, Vol. 50, No. 4, pp. 521–532, July-August, 2011.

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Kartashova, A.V. Antivarieties of unars. Algebra Logic 50, 357–364 (2011). https://doi.org/10.1007/s10469-011-9147-4

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  • DOI: https://doi.org/10.1007/s10469-011-9147-4

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