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Fundam. Prikl. Mat., 2014, Volume 19, Issue 6, Pages 153–189 (Mi fpm1619)  

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

Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus

V. V. Sidorov

Vyatka State University of Humanities, Kirov

Abstract: Isomorphisms $\varphi$ of semirings $C^\vee(X)$ of continuous nonnegative functions over an arbitrary Hewitt space $X$ with the condition $\varphi(\mathbb R^+)=\mathbb R^+$ are characterized in this work. It is proved that any isomorphism of lattices of all subalgebras of semirings $C^\vee(X)$ and $C^\vee(Y)$ is induced by a unique isomorphism of semirings excepting the case of one- and two-point Tychonovization of spaces.

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English version:
Journal of Mathematical Sciences (New York), 2017, 221:3, 409–435

Bibliographic databases:

UDC: 512.556

Citation: V. V. Sidorov, “Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus”, Fundam. Prikl. Mat., 19:6 (2014), 153–189; J. Math. Sci., 221:3 (2017), 409–435

Citation in format AMSBIB
\Bibitem{Sid14}
\by V.~V.~Sidorov
\paper Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 6
\pages 153--189
\mathnet{http://mi.mathnet.ru/fpm1619}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431906}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 221
\issue 3
\pages 409--435
\crossref{https://doi.org/10.1007/s10958-017-3235-5}


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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, A. V. Mikhalev, V. V. Sidorov, “Semirings of continuous functions”, J. Math. Sci., 237:2 (2019), 191–244  mathnet  crossref
    2. V. V. Sidorov, “Isomorphisms of lattices of subalgebras of semifields of positive continuous functions”, Siberian Math. J., 60:3 (2019), 526–541  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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