On a theorem of McCoy

Abstract

We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring $R$ satisfies McCoy's theorem of skew Hurwitz series.

Keywords

• skew hurwitz series ring
• $\omega$-compatible ring
• skew hurwitz serieswise
• quasi-armendariz rings
• zip ring
• app ring