Armendariz rings and reduced rings (Q1970962)

According to \textit{D. D. Anderson} and \textit{V. Camillo} [Commun. Algebra 26, No. 7, 2265-2272 (1998; Zbl 0915.13001)], a ring \(R\) is called Armendariz if whenever polynomials \(f(x)=a_0+a_1x+\cdots+a_m x^m\) and \(g(x)=b_0+b_1x+\cdots+b_nx^n\) in \(R[x]\) satisfy \(f(x)g(x)=0\), then \(a_ib_j=0\) for each \(i\), \(j\). It is shown that if a ring \(R\) is Armendariz, then \(R\) is PP (resp. Baer) if and only if \(R[x]\) is PP (resp. Baer). Also it is shown that a semisimple Artinian ring \(R\) is Armendariz if and only if \(R\) is a direct sum of division rings.