Nil Armendariz rings of Hurwitz series type ۱

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.

کلیدواژه ها:

nil Armendariz ring ، nil Armendariz ring of Hurwitz series type ، nil Armendariz ring of skew Hurwitz series type