朱孝璋.质环的求导和交换性[J].数学研究及应用,1990,10(2):167~170
质环的求导和交换性
Derivations and Commutativity of Prime Rings
投稿时间:1987-12-02  
DOI:10.3770/j.issn:1000-341X.1990.02.003
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朱孝璋 天津教育学院 
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      In this paper, we generalize some corresponding results of [1-4]. We obtain the main results as the following:Theorem 1 Let R be a prime ring of characteristic not 2 with nontrivial derivations d1,d2 and let U be a nonzero ideal of R . If C is the center of R, then the following conditions are equivalent : (i)d1,d2(x)∈C for all x∈U; (ii) [d1(x),d2(y)]∈C for all x,y∈U; (iii) d1(x)d2(y) d2(x)d1(y)∈C for all x,y∈U; (iv) R is commutative.Theorem 2 Let R be a prime ring with nontrivial derivations d1,d2,…, dn and U be a nonzero ideal of R. Let C be the center of R. If d1(x1)d2(x2)…dn(xn)∈C for all x1, x2…xn)∈U, then R is commutative.
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