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Mat. Sb., 2016, Volume 207, Number 9, Pages 91–110 (Mi msb8609)  

This article is cited in 1 scientific paper (total in 1 paper)

Definability of semifields of continuous positive functions by the lattices of their subalgebras

V. V. Sidorov

Vyatka State University, Kirov

Abstract: We consider the lattice $\mathbb{A}(U(X))$ of subalgebras of a semifield $U(X)$ of continuous positive functions on an arbitrary topological space $X$ and its sublattice $\mathbb{A}_1(U(X))$ of subalgebras with unity. The main result of the paper is the proof of the definability of any semifield $U(X)$ both by the lattice $\mathbb{A}(U(X))$ and by its sublattice $\mathbb{A}_1(U(X))$.
Bibliography: 12 titles.

Keywords: semifield of continuous functions, subalgebra, lattice of subalgebras, isomorphism, Hewitt space.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1375.2014/K
The paper was prepared within the framework of the state commission of the Ministry for Education and Science of the Russian Federation (project no. 1.1375.2014/K).


DOI: https://doi.org/10.4213/sm8609

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English version:
Sbornik: Mathematics, 2016, 207:9, 1267–1286

Bibliographic databases:

Document Type: Article
UDC: 512.556
MSC: Primary 54C30; Secondary 12K10, 46A40, 46E05, 46J30
Received: 01.10.2015 and 09.03.2016

Citation: V. V. Sidorov, “Definability of semifields of continuous positive functions by the lattices of their subalgebras”, Mat. Sb., 207:9 (2016), 91–110; Sb. Math., 207:9 (2016), 1267–1286

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Sidorov, “Determinability of Hewitt spaces by the lattices of subalgebras with unit of semifields of continuous positive functions with max-plus”, Lobachevskii J. Math., 38:4 (2017), 741–750  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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