FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 63-103

**Isomorphisms of lattices of subalgebras of semirings of continuous
nonnegative functions**

E. M. Vechtomov

V. V. Sidorov

Abstract

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In this work, lattice isomorphisms of semirings $C+(X)$ of
continuous nonnegative functions over an arbitrary topological
space $X$
are characterized.
It is proved that any isomorphism of lattices of all subalgebras with
a unit of semirings $C+(X)$ and
$C+(Y)$ is induced
by a unique isomorphism of semirings.
The same result is also correct for lattices of all subalgebras
excepting the case of two-point Tychonovization of spaces.

Location: http://mech.math.msu.su/~fpm/eng/k10/k103/k10303h.htm

Last modified: March 24, 2011