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頁籤選單縮合
題名 | A Property for Simple Ring Implying Field and Commutativity of Rings=一性質使單純環成體及環的交換 |
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作者 | 嚴正德; | 書刊名 | 中原學報 |
卷期 | 21 1992.12[民81.12] |
頁次 | 頁8-11 |
分類號 | 313.28 |
關鍵詞 | 交換; 成體; 單純環; 環; 弱交換環; 質環; 半質環; 半直接不可約環; 扭轉自由環; Weakly commutative ring; Simple ring; Prime ring; Semiprime ring; Subdirectly irreducible ring; Torsion free ring; |
語文 | 英文(English) |
中文摘要 | 它是被證明:若R是一單純環,則廣義中心G(R)={a∈R:對任一y∈R.存在n=n(a,y)∈Z使得ay=nya}是等於中心Z(R);此外R是一體若G(R)=R。我們也證明任一弱交換環(G(R)=R)且有單位元素是交換的或是每一非零元素是有限加法次。沒有單位元素,R是交換的若它是一半質環。此外,R是交換或反交換若R是扭轉自由。 |
英文摘要 | It is shown that if R is a simple ring, then the generalized center G(R)={a∈R: for every y in R, there exists an integer n=n(a, y)∈Z such that ay=nya} is equal to the center Z(R); moreover, R is a field if G(R)=R. We also prove that every weakly commutative ring (G(R) =R) with identity is either commutative or every nonzero elememt is of finite additive order. Without the identity, R is commutative if it is a semiprime ring. Furthermore, R is either commutative or anticommutative if R is torsion free. |
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