Central Armendariz Rings

Agayev N., Gungoroglu G., Harmanci A., HALICIOĞLU S.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.34, no.1, pp.137-145, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2011
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.137-145
  • Hacettepe University Affiliated: Yes

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 xn and n >= 2. Among others we also show that R is a reduced ring if and only if the matrix ring T,2(R) is central Armendariz, for a natural number n >= 3 and k = [n/2].