Nil Armendariz rings of Hurwitz series type 1

نویسندگان
Sabzipour, Kianoosh ID 1
Haj Seyyed Javadi, Hamid ID 2

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

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

doi
10.22075/ijnaa.2024.35416.5275
چکیده

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.

کلیدواژه‌ها
nil Armendariz ring, nil Armendariz ring of Hurwitz series type, nil Armendariz ring of skew Hurwitz series type