Bulletin of the
Korean Mathematical Society BKMS

We in this note introduce a concept, so called {\it $\pi$-Armendariz ring}, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of $\pi$-Armendariz rings, constructing typical examples. We next extend the class of $\pi$-Armendariz rings, through various ring extensions.

Keywords: $\pi$-Armendariz ring, 2-primal ring, Armendariz ring, nilpotent element

MSC numbers: 16D25, 16N40, 16S36