Original scientific paper

On nilpotent elements in a nearring of polynomials

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

Abstract

For a ring $R$, $R[x]$ is a left nearring under addition and substitution, and we denote it by ($R[x],+,\circ$).
In this note, we show that if $nil(R)$ is a locally nilpotent ideal of $R$,
then $nil(R[x],+,\circ)=nil(R)_0[x]$, 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 $nil(R[x],+,\circ)=nil(R)_0[x]$.

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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