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Sbornik: Mathematics, 2016, Volume 207, Issue 9, Pages 1267–1286
DOI: https://doi.org/10.1070/SM8609 (Mi sm8609) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

V. V. Sidorov

Vyatka State University, Kirov
English version PDF (493 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM8609
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).
Received: 01.10.2015 and 09.03.2016
Bibliographic databases:
Document Type: Article
UDC: 512.556
MSC: Primary 54C30; Secondary 12K10, 46A40, 46E05, 46J30
Language: English
Original paper language: Russian
Citation: V. V. Sidorov, “Definability of semifields of continuous positive functions by the lattices of their subalgebras”, Sb. Math., 207:9 (2016), 1267–1286
Citation in format AMSBIB
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\paper Definability of semifields of continuous positive functions by the lattices of their subalgebras
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\pages 1267--1286
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  • https://doi.org/10.1070/SM8609
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:126
    English version PDF:19
    References:70
    First page:36
     
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