International Journal of Nonlinear Analysis and Applications

Nil Armendariz rings of Hurwitz series type 1

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Tarbiat Modares University, Tehran, Iran

2 Department of Mathematics and Computer Science, Shahed University, Tehran, Iran

Abstract

In this paper, we study the structure of the set of nilpotent elements in Armendariz rings of Hurwitz series type and introduce nil Armendariz as a generalization. It is proved that a ring $R$ is nil Armendariz of Hurwitz series type if and only if $R$ has characteristic zero and $Nil(R)$ is an ideal. We provide many examples of nil Armendariz rings of Hurwitz series type and extend the class of nil Armendariz rings of Hurwitz series type through various ring extensions.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 9
September 2025
Pages 87-93
  • Receive Date: 23 July 2024
  • Accept Date: 27 September 2024