FUNDAMENTALNAYA
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

Abstract

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In this paper, we describe automorphisms of the
lattice $$**A** of all subalgebras
of the semiring $$**R**^{+}[x] of
polynomials in one variable over the semifield $$**R**^{+} of
nonnegative real numbers.
It is proved that any automorphism of the lattice $$**A** is generated by an
automorphism of the semiring $$**R**^{+}[x]
that is induced by a substitution $\$\; x\; \backslash mapsto\; px\; \$$ for some
positive real number $p$.
It follows that the automorphism group of the lattice $$**A** is isomorphic to
the group of all positive real numbers with multiplication.
A technique of unigenerated subalgebras is applied.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k113/k11307h.htm

Last modified: May 4, 2012