Some results about ideals satisfying the condition Cn

We introduce, in this paper, a condition Cn that can be viewed as a generalization of the conditions C2 investigated recently by the present authors in [1,2,9,10]. We use this condition to give some results in the study of linear equivalence of ideal topologies and valuation ideals. Moreover, we present the notion of Cn-maximal ideals, and we show that every ideal satisfying the condition Cn is contained in a Cn-maximal ideal.