The paper under review studies the following generalization of prime ideals. For positive integers \(m > n\), the authors define an \((m,n)\)-absorbing ideal (of a commutative unital ring) to be a proper ideal \(I\) such that any product of \(m\) nonunits that lies in \(I\) has some length-\(n\) subproduct in \(I\). For example, a \((2,1)\)-absorbing ideal is simply a prime ideal, and \((n+1,n)\)-absorbing ideals are the same thing as the \(n\)-absorbing ideals previously defined by D. F. Anderson and A. Badawi [Comm. Algebra 39, No. 5, 1646–1672 (2011; Zbl 1355.13004)] and further studied by several others in many subsequent papers. The majority of the paper under review is devoted to showing that many of the results of Anderson and Badawi carry over to \((m,n)\)-absorbing ideals. The present paper follows this past paper very closely. Its main completely original contribution is its introduction of “minimal \((m,n)\)-absorbing ideals”, which are defined analogously to minimal primes. The authors present their material with laudable economy. In the reviewer’s opinion, it would make sense to read the paper of Anderson and Badawi [loc. cit.] as a first paper on this topic (the motivating examples are especially helpful), and then proceed to the present paper if interested in the \((m,n)\)-absorbing generalization.