The endotopism spectrum of an equivalence (in Russian) |
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| Author |
e.a.rom@mail.ru
Luhansk Taras Shevchenko National University
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| Abstract |
We study semigroups of endotopisms of six types for an arbitrary equivalence relation.
We calculate an endotopism spectrum of an equivalence relation on a finite set relative to its
endotopisms.
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| Keywords |
endotopism; equivalence relation; endospectrum of binary relation
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| DOI |
doi:10.15330/ms.46.1.3-12
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| Reference |
1. Schein B., Teclezghi B. Endomorphisms of finite full transformation semigroups// Proc. Amer. Math.
Soc. – 1998. – ¹126. – P. 2579–2587.
2. Mazorchuk V. Endomorphisms of $B_n$, $PB_n$ and $C_n$// Comm. Algebra. – 2002. – ¹30. – P. 3489–3513. 3. Molchanov A.V. Semigroups of endomorphisms of weak p-hypergraphs// Isv. Vyssh. Uchebn. Zaved. Mat. – 2000. – ¹3(454). – P. 80–83. (in Russian) 4. Zhuchok Yu.V. The monoid of endomorphisms of disconnected hypergraphs// Algebra and Discrete Mathematics. – 2013. – ¹16. – P. 134–150. 5. Gluskin L.M. The semigroup of isotonne transformations// Uspehi. Mat. Nauk. – 1961. – ¹5. – P. 157– 162. (in Russian) 6. Araujo J., Konieczny J. Dense relations are determined by their endomorphisms monoids// Semigroup Forum. – 2005. – ¹70. – P. 302–306. 7. Shneperman L.B. Semigroups of endomorphisms of quasiordered sets// Uch. Zap. LGPI im. A. I. Gertsena. – 1962. – V. 238. – P. 21–37. (in Russian) 8. Popov B.V. Endomorphism semigroups of reflexive binary relations// Uch. Zap. LGPI im. A. I. Gertsena. – 1967. – V. 302. – P. 116–123. (in Russian) 9. Popov B.V. Endotopism semigroups of $\mu$-ary relations// Uch. Zap. LGPI im. A. I. Gertsena. – 1965. – V. 274. – P. 184–201. (in Russian) 10. Kurosh A.G. General algebra (lectures 1969-70 school year). – Ì.: Nauka, 1974, 160 p. (in Russian) 11. Zhuchok Yu.V., Toichkina E.A. Correspondences of the semigroup of endomorphisms of an equivalence relation// Mat. Zametki. – 2015. – V. 97, ¹2. – P. 217–230. (in Russian) 12. Zhuchok Yu.V. Endotypes of equivalence relations// Quasigroups and Related Systems. – 2014. – ¹22. – P. 295–300. 13. Zhuchok Yu.V., Toichkina E.A. The endotopism semigroups of an equivalence relation// Mat. Sbornik. – 2014. – V.205, ¹5. – P. 37–54. (in Russian) 14. Bottcher M., Knauer U. Endomorphism spectra of graphs// Discrete Mathematics. – 1992. – ¹109. – P. 45–57. |
| Pages |
3-12
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| Volume |
46
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| Issue |
1
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |