We study the interplay of the Golomb topology and the algebraic structure in polynomial rings K [X] over a field K. In particular, we focus on infinite fields K of positive characteristic such that the set of irreducible polynomials of K [X] is dense in the Golomb space G(K [X]). We show that, in this case, the characteristic of K is a topological invariant, and that any self-homeomorphism of G(K [X]) is the composition of multiplication by a unit and a ring automorphism of K [X].
The Golomb topology of polynomial rings, II
Spirito D.
2023-01-01
Abstract
We study the interplay of the Golomb topology and the algebraic structure in polynomial rings K [X] over a field K. In particular, we focus on infinite fields K of positive characteristic such that the set of irreducible polynomials of K [X] is dense in the Golomb space G(K [X]). We show that, in this case, the characteristic of K is a topological invariant, and that any self-homeomorphism of G(K [X]) is the composition of multiplication by a unit and a ring automorphism of K [X].File in questo prodotto:
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