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Algebra Logika, 2017, Volume 56, Number 4, Pages 486–505 (Mi al810)  

$P$-stable polygons

A. A. Stepanovaab, D. O. Ptakhova

a School of Natural Sciences, Far Eastern Federal University, ul. Sukhanova 8, Vladivostok, 690091 Russia
b Institute of Applied Mathematics, ul. Radio 7, Vladivostok, 690041 Russia

Abstract: $P$-stable polygons are studied. It is proved that the property of being $(P,s)$-, $(P,a)$-, and $(P,e)$-stable for the class of all polygons over a monoid $S$ is equivalent to $S$ being a group. We describe the structure of $(P,s)$-, $(P,a)$-, and $(P,e)$-stable polygons $SA$ over a countable left-zero monoid $S$ under the condition that the set $A\setminus SA$ is indiscernible over a right-zero monoid.

Keywords: $P$-stable theories, polygons, $P$-stable polygons.

DOI: https://doi.org/10.17377/alglog.2017.56.407

Full text: PDF file (218 kB)
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English version:
Algebra and Logic, 2017, 56:4, 324–336

Bibliographic databases:

UDC: 510.67+512.56
Received: 14.12.2015

Citation: A. A. Stepanova, D. O. Ptakhov, “$P$-stable polygons”, Algebra Logika, 56:4 (2017), 486–505; Algebra and Logic, 56:4 (2017), 324–336

Citation in format AMSBIB
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\by A.~A.~Stepanova, D.~O.~Ptakhov
\paper $P$-stable polygons
\jour Algebra Logika
\yr 2017
\vol 56
\issue 4
\pages 486--505
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\crossref{https://doi.org/10.17377/alglog.2017.56.407}
\transl
\jour Algebra and Logic
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\vol 56
\issue 4
\pages 324--336
\crossref{https://doi.org/10.1007/s10469-017-9453-6}
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  • Алгебра и логика Algebra and Logic
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