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

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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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
2. V. V. Sidorov, “Isomorphisms of lattices of subalgebras of semifields of positive continuous functions”, Siberian Math. J., 60:3 (2019), 526–541
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