Let R = K[x, σ] be the skew polynomial ring over a field K, where σ is an automorphism of K of finite order. We show that prime elements in R correspond to completely prime one-sided ideals – a notion introduced by Reyes in 2010. This extends the natural correspondence between prime elements and prime ideals in commutative polynomial rings.

中文翻译：

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在斜多项式环中完全取单面理想

让R=ķ[X,σ] 是域上的偏斜多项式环ķ， 在哪里σ是一个自同构ķ有限阶。我们证明了素数在R对应于完全素数单边理想——Reyes 在 2010 年引入的一个概念。这扩展了交换多项式环中素数元素和素数理想之间的自然对应关系。