The Structure of a Class of Rings
Received:August 27, 1992  
Key Words: Rings   subdirect sum   words.  
Fund Project:
Author NameAffiliation
Guo Hiuzhan Dept. of Math.
China University of Mining and Technology
Xuzhou 221008 
Wei Bing Dept. of Math.
China University of Mining and Technology
Xuzhou 221008 
Yang Yongguo Dept. of Math.
China University of Mining and Technology
Xuzhou 221008 
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Abstract:
      Let R be a ring, and N the set of all nilpotent elements of R. We prove thefollowingTheorem if a rinq R satisfies the following condition: for all x1…,xk in R, there existwords ω2 = ω1(x2,…,xk ) and ω2 = ω2(x1…,xk-1 depending on x1 …,xk such that|ω1|xk> 1,|ω2|>1, and|ω1|≠|ω2|. Suppose that x1 ω1 (x2…,xk) = ω2( x1…,xk-1)xk where k >1 is a fixed integer. Then(1) N jorms an ideal of R,(2) R = N + R1, where R1 is isomorphic to a subdirect sum of fields. In particular, if N is commutative, then R is commutative.
Citation:
DOI:10.3770/j.issn:1000-341X.1994.04.009
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