Volume 34 • Number 1 • 2011   • Central Armendariz Rings Nazim Agayev, Gonca Güngöroglu, A. Harmanci and S. Halicioglu Abstract. We introduce the notion of central Armendariz rings which are a generalization of Armendariz rings and investigate their properties. We show that the class of central Armendariz rings lies strictly between classes of Armendariz rings and abelian rings. For a ring \(R\), we prove that \(R\) is central Armendariz if and only if the polynomial ring \(R[x]\) is central Armendariz if and only if the Laurent polynomial ring \(R[x, x^{-1}]\) is central Armendariz. Moreover, it is proven that if \(R\) is reduced, then \(R[x]/(x^{n})\) is central Armendariz, the converse holds if \(R\) is semiprime, where \((x^n)\) is the ideal generated by \(x^n\) and \(n\geq 2\). Among others we also show that \(R\) is a reduced ring if and only if the matrix ring \(T_{n}^{n-2}(R)\) is central Armendariz, for a natural number \(n \geq 3\) and \(k=[n/2]\). 2010 Mathematics Subject Classification: 16U80. Full text: PDF