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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 2, Pages 12–18 (Mi vuu214)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

About prime ideals in semirings of continuous function with values in unit segment

E. M. Vechtomov, E. N. Lubiagina

Vyatka State University of Humanities, Kirov, Russia

Abstract: The properties of the prime ideals in semirings of the continuous functions on topological spaces with values in [0,1] are researches. Maximal ideals of the semirings of continuous [0,1]-valued functions are described. The characterizations of the compacts are received in terms of semiring of the functions. It is shown that the theory of ideals in considered semirings differs from the case of rings of continuous functions.

Keywords: semiring, unit interval, compact, semiring of the continuous functions, prime ideal of the semiring.

Full text: PDF file (157 kB)
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UDC: 512.566
MSC: 16Y60, 12K10
Received: 20.05.2011

Citation: E. M. Vechtomov, E. N. Lubiagina, “About prime ideals in semirings of continuous function with values in unit segment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2, 12–18

Citation in format AMSBIB
\Bibitem{VecLub11}
\by E.~M.~Vechtomov, E.~N.~Lubiagina
\paper About prime ideals in semirings of continuous function with values in unit segment
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 2
\pages 12--18
\mathnet{http://mi.mathnet.ru/vuu214}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vechtomov E.M., Lubyagina E.N., “Reshetki nepreryvnykh funktsii so znacheniyami v edinichnom otrezke”, Vestnik Syktyvkarskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika, 2011, no. 14, 3–20  elib
    2. E. M. Vechtomov, E. N. Lubyagina, “Zamknutye idealy i zamknutye kongruentsii polukolets nepreryvnykh $[0,1]$-znachnykh funktsii s topologiei potochechnoi skhodimosti”, Tr. IMM UrO RAN, 19, no. 3, 2013, 83–93  mathnet  mathscinet  elib
    3. E. M. Vechtomov, A. V. Mikhalev, V. V. Sidorov, “Semirings of continuous functions”, J. Math. Sci., 237:2 (2019), 191–244  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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