On a ring property unifying reversible and right duo rings. (Q2861457)

In this paper, the notion of right Armendariz-like ring is studied. Namely, an associative ring \(R\) with identity is called right Armendariz-like, if for any polynomials \(f(x)=\sum^m_{ i=0}\alpha_ix^i,g(x)=\sum^n_{j=0}b_jx^j\) over \(R\) with \(f(x)g(x)=0\) there exists \(r\in R\) such that \(g(x)r\neq 0\) and \(a_ib_jr=0\) for any \(i,j\). The authors find a way to construct a right Armendariz-like ring that is not Armendariz. Moreover, there is an example of a strongly right McCoy ring but not right Armendariz-like. Also, some properties of right Armendariz-like rings that are analogous to known results about Armendariz rings are proved. In particular, it is shown that \(R\) is a right Armendariz-like ring iff so is \(R[x]\).