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Fundam. Prikl. Mat., 2012, Volume 17, Issue 4, Pages 53–82 (Mi fpm1421)  

This article is cited in 2 scientific papers (total in 2 papers)

The semiring of continous $[0,1]$-valued functions

E. M. Vechtomov, E. N. Lubyagina

Vyatka State University of Humanities

Abstract: In this paper, we study the properties of prime ideals in semirings of continuous functions with values in the unit interval $[0,1]$ on topological spaces. We describe maximal and pure ideals of such semirings. We study homomorphisms of semirings of continuous $[0,1]$-valued functions. In terms of semirings of functions we characterize some properties of compacta. We show that the theory of ideals in these semirings differs from the case of rings of continuous functions.

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English version:
Journal of Mathematical Sciences (New York), 2013, 191:5, 633–653

UDC: 512.556

Citation: E. M. Vechtomov, E. N. Lubyagina, “The semiring of continous $[0,1]$-valued functions”, Fundam. Prikl. Mat., 17:4 (2012), 53–82; J. Math. Sci., 191:5 (2013), 633–653

Citation in format AMSBIB
\Bibitem{VecLub12}
\by E.~M.~Vechtomov, E.~N.~Lubyagina
\paper The semiring of continous $[0,1]$-valued functions
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 4
\pages 53--82
\mathnet{http://mi.mathnet.ru/fpm1421}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 191
\issue 5
\pages 633--653
\crossref{https://doi.org/10.1007/s10958-013-1348-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884989648}


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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. E. M. Vechtomov, N. V. Shalaginova, “Semirings of continuous $(0,\infty]$-valued functions”, J. Math. Sci., 233:1 (2018), 28–41  mathnet  crossref  elib
    2. E. M. Vechtomov, A. V. Mikhalev, V. V. Sidorov, “Semirings of continuous functions”, J. Math. Sci., 237:2 (2019), 191–244  mathnet  crossref
  • Фундаментальная и прикладная математика
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