for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In this paper our goal to thoroughly determine the rings in which each non-unit element is a product of nilpotent and quasi-idempotent.

In this paper, we show that one can construct a \begin{document}$ G $\end{document}-code from group rings is reversible. Specifically, given with subgroup of order half the ambient an element its own inverse outside subgroup, give ordering elements for which id="M4">\begin{document}$ $\end{document}</tex-...