http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Identities with additive mappings in semiprime rings
Ajda Fosner,Nadeem Ur Rehman 대한수학회 2014 대한수학회보 Vol.51 No.1
The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R → R is an additive mapping satisfying the relation [f(x), xn] = 0 for all x ∈ R. Then f is commuting on R.
IDENTITIES WITH ADDITIVE MAPPINGS IN SEMIPRIME RINGS
Fosner, Ajda,Ur Rehman, Nadeem Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.
A NOTE ON SKEW DERIVATIONS IN PRIME RINGS
De Filippis, Vincenzo,Fosner, Ajda Korean Mathematical Society 2012 대한수학회보 Vol.49 No.4
Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.