我們考慮由環的非交換性質所導出的圖之完全子圖，然後證明了在一個無窮且非交換的prime ring所導出的圖會包含一個無窮的完全子圖。我們也計算一些具體的圖之clique number和chromatic number。

We consider complete subgraphs of the graph induced by the noncommutativity of a ring, and prove that the graph induced by an infinite noncommutative prime ring contains an infinite complete subgraph. We also compute the clique number and the chromatic number of the graphs induced by some concrete graphs.

1 Introduction.......................................................4
2 Preliminaries ...................................................5
3 The result of Bell, Klein and Kappe .............9
4 Discussions ..................................................12
References .......................................................29

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