We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show that if K is an algebraic extension of a finite field and K′ is a field of the same characteristic, then the Golomb spaces of K[X] and K′[X] are homeomorphic if and only if K and K′ are isomorphic.
The Golomb Topology of Polynomial Rings
Spirito D.
2021-01-01
Abstract
We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show that if K is an algebraic extension of a finite field and K′ is a field of the same characteristic, then the Golomb spaces of K[X] and K′[X] are homeomorphic if and only if K and K′ are isomorphic.File in questo prodotto:
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