论文标题
研究类似分区的财产
Study of a division-like property
论文作者
论文摘要
我们引入了非交通戒指的类似薄的分区的属性：如果对于所有非零$ a，x $，存在$ x = ab+ca $，则非平凡环为Fadelian。我们证明了Fadelian环的性质，并构建了不是分裂环的示例，以及非诺瑟式和非俄罗斯式示例。我们还在精益助手的助手中正式化了其中一些结果。
We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings which are not division rings, as well as non-Noetherian and non-Ore examples. We have also formalized some of these results in the Lean proof assistant.
