I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 3, PAGES 85-96
Automorphisms of the lattice of all subalgebras of the semiring of
polynomials in one variable
V. V. Sidorov
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In this paper, we describe automorphisms of the
lattice of all subalgebras
of the semiring of
polynomials in one variable over the semifield of
nonnegative real numbers.
It is proved that any automorphism of the lattice is generated by an
automorphism of the semiring
that is induced by a substitution for some
positive real number .
It follows that the automorphism group of the lattice is isomorphic to
the group of all positive real numbers with multiplication.
A technique of unigenerated subalgebras is applied.
Last modified: May 4, 2012