EP elements of $\mathbb{Z}[x]/(x^2+x)$

Abstract

In this paper, we first show that the quotient ring $\mathbb{Z}[x]/(x^2+x)$ is an involution-ring with the involution $*$ given by $(a_1+a_2x)^*=a_1-a_2-a_2x$, where $a_1,a_2\in\mathbb{Z}$. Then, we explicitly determine all invertible elements, regular elements, MP-inverses, group invertible elements, EP elements and SEP elements of $\mathbb{Z}[x]/(x^2+x)$. Furthermore, we give a new characterization for Abel rings.