Annihilating content polynomials and EM-rings

Abstract

Let [Formula: see text] be a commutative ring. A polynomial [Formula: see text] is an annihilating content (AC) polynomial if [Formula: see text] where [Formula: see text] and [Formula: see text] is a nonzerodivisor and [Formula: see text] is an EM-ring if each [Formula: see text] is an AC polynomial. In this paper, we investigate AC polynomials and EM-rings and extensions to modules. For example, we show that [Formula: see text] is an EM-ring if and only if every linear polynomial is an AC polynomial if and only if for each finitely generated ideal [Formula: see text] of [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] is a finitely generated ideal of [Formula: see text] with [Formula: see text]. Special attention is given to the case when [Formula: see text] is Noetherian where such rings are characterized by the property that each associated prime is principal.