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

View as HTML     View as gif image

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