EP elements of Z[x]/(x2+x)

Abstract

In this paper, we first show that the quotient ring Z[x]/(x2 + x) is an involution-ring with the involution ? given by (a1 +a2x)* = a1 ?a2 ?a2x, where a1, a2 ? Z. Then, we determine explicitly all invertible elements, regular elements, MP-inverses, group invertible elements, EP elements and SEP elements of Z[x]/(x2 + x). Furthermore, we give a new characterization for Abel rings.