论文标题
多项式环的Golomb拓扑，II
The Golomb topology of polynomial rings, II
论文作者
论文摘要
我们研究了golomb拓扑结构的相互作用和多项式环的代数结构$ k [x] $在field $ k $上。特别是，我们专注于无限字段$ k $的积极特征，以便在Golomb Space $ G（k [x]）$中，$ k [x] $的不可约多项式的集合是密集的。我们表明，在这种情况下，$ k $的特征是拓扑不变的，并且任何$ g（k [x]）$的自塑形性是乘以单位乘法的组成，而$ k [x] $的环形自动形态。
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 $K[X]$.
