JournalsrmiVol. 30, No. 3pp. 1073–1088

On a characterization of distributive rings via saturations and its applications to Armendariz and Gaussian rings

  • Ryszard Mazurek

    Białystok University of Technology, Poland
  • Michał Ziembowski

    Warsaw University of Technology, Poland
On a characterization of distributive rings via saturations and its applications to Armendariz and Gaussian rings cover
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Abstract

In this paper we apply Ferrero–Sant’Ana’s characterization of right distributive rings via saturations to prove that all right distributive rings are Armendariz relative to any unique product monoid. As an immediate consequence we obtain that all right distributive rings are Armendariz. We apply this result to give a new proof of the well-known fact that all right duo right distributive rings are right Gaussian. We also show that for any nontrivial unique product monoid SS, the class of Armendariz rings relative to SS is contained in the class of Armendariz rings, and we present an example of a unique product monoid SS for which this containment is strict.

Cite this article

Ryszard Mazurek, Michał Ziembowski, On a characterization of distributive rings via saturations and its applications to Armendariz and Gaussian rings. Rev. Mat. Iberoam. 30 (2014), no. 3, pp. 1073–1088

DOI 10.4171/RMI/807