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Original scientific paper

On nilpotent elements in a nearring of polynomials

Ebrahim Hashemi ; Department of Mathematics, Shahrood University of Technology, Shahrood, Iran


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Abstract

For a ring R, R[x] is a left nearring under addition and substitution, and we denote it by (R[x],+,).
In this note, we show that if nil(R) is a locally nilpotent ideal of R,
then nil(R[x],+,)=nil(R)0[x], where nil(R) is the set of nilpotent elements of R and nil(R)0[x] is the 0-symmetric left nearring of polynomials with coefficients in nil(R). As a corollary, if R is a 2-primal ring, then nil(R[x],+,)=nil(R)0[x].

Keywords

Armendariz rings; nearring of polynomials; nilpotent elements; insertion of factors property; 2-primal rings

Hrčak ID:

83079

URI

https://hrcak.srce.hr/83079

Publication date:

12.6.2012.

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