A question about higher order <i>z</i>-ideals in commutative rings

Abstract

Let D be a principal ideal domain, p an irreducible element of D and m a nonzero positive integer. In this paper we show that the ring D/_p^mD answers the question asked by Dube and Ighedo in [1] concerning higher order z-ideals.

Mathematics Subject Classification (2010): 13A15, 13F10.

Keywords: z-ideal, higher order z-ideal