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

被引：1
作者：
Sidorov, V. V. [1 ]
机构：
[1] Vyatka State Univ, Kirov, Russia
来源：
SBORNIK MATHEMATICS | 2016年 / 207卷 / 09期
关键词：
semifield of continuous functions; subalgebra; lattice of subalgebras; isomorphism; Hewitt space;
D O I：
10.1070/SM8609
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the lattice A(U(X)) of subalgebras of a semifield U(X) of continuous positive functions on an arbitrary topological space X and its sublattice 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 A(U(X)) and by its sublattice A(1)(U(X)).
引用
收藏
页码：1267 / 1286
页数：20
相关论文
共 12 条
[1]  
[Anonymous], 1978, Pure and Applied Mathematics
[2]  
Engelking R, 1977, MONOGR MAT, V60
[3]  
Gelfand I, 1939, CR ACAD SCI URSS, V22, P11
[4]  
GILLMAN L, 1960, GRAD TEXTS MATH, V43
[5]  
Golan J.S., 2010, SEMIRINGS THEIR APPL, DOI [10.1007/978-94-015-9333-5, DOI 10.1007/978-94-015-9333-5]
[6]   RINGS OF REAL-VALUED CONTINUOUS FUNCTIONS .1. [J].
HEWITT, E .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1948, 64 (JUL) :45-99
[7]  
Varankina V. I., 1998, FUNDAM PRIKL MAT, V4, p[2, 493]
[8]  
Vechtomov EM, 2015, T I MAT MEKH URO RAN, V21, P78
[9]  
Vechtomov E. M., 2010, J MATH SCI, V16, p[3, 63], DOI [DOI 10.1007/s10958-011-0511-7, 10.1007/s10958-011-0511-7]
[10]  
Vechtomov E.M., 1994, J MATH SCI-U TOKYO, V71, P2364, DOI 10.1007/BF02111022
12