Journal of the
Korean Mathematical Society JKMS

Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called {\it IMIP} when it satisfies such property. It is shown that the Dorroh extension of $A$ by $K$ is an IMIP ring if and only if $A$ is an IFP ring without identity, where $A$ is a nil algebra over a field $K$. The structure of an IMIP ring is studied in relation to various kinds of rings which have roles in noncommutative ring theory.

Keywords: IMIP ring, maximal ideal, IFP ring, Dorroh extension, idempo\-tent

MSC numbers: 16D25