Geodesic
Definability of semifields of continuous positive functions by the lattices of their subalgebras
Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1267-1286

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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, lattice of subalgebras, Hewitt space.
Mots-clés : subalgebra, isomorphism 
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     author = {V. V. Sidorov},
     title = {Definability of semifields of continuous positive functions by the lattices of their subalgebras},
     journal = {Sbornik. Mathematics},
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     volume = {207},
     number = {9},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_9_a3/}
}
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V. V. Sidorov. Definability of semifields of continuous positive functions by the lattices of their subalgebras. Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1267-1286. http://geodesic.mathdoc.fr/item/SM_2016_207_9_a3/