Email this article Polygons with a (P, 1)-Stable Theory
- Authors: Ptakhov D.O.1
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Affiliations:
- School of Natural Sciences, Far Eastern Federal University
- Issue: Vol 56, No 6 (2018)
- Pages: 473-478
- Section: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234064
- DOI: https://doi.org/10.1007/s10469-018-9469-6
- ID: 234064
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Abstract
Polygons with a (P, 1)-stable theory are considered. A criterion of being (P, 1)-stable for a polygon is established. As a consequence of the main criterion we prove that a polygon SS, where S is a group, is (P, 1)-stable if and only if S is a finite group. It is shown that the class of all polygons with monoid S is (P, 1)-stable only if S is a one-element monoid. (P, 1)-stability criteria are presented for polygons over right and left zero monoids.
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About the authors
D. O. Ptakhov
School of Natural Sciences, Far Eastern Federal University
Author for correspondence.
Email: ptaxov@mail.ru
Russian Federation, ul. Sukhanova 8, Vladivostok, 690091
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