Izvorni znanstveni članak
On nilpotent elements in a nearring of polynomials
Ebrahim Hashemi
; Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
Sažetak
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 $nil(R[x],+,\circ)=nil(R)_0[x]$.
Ključne riječi
Armendariz rings; nearring of polynomials; nilpotent elements; insertion of factors property; 2-primal rings
Hrčak ID:
83079
URI
Datum izdavanja:
12.6.2012.
Posjeta: 1.346 *