Abstract
We introduce, in this paper, a condition C-n that can be viewed as a generalization of the conditions C-2 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 C-n-maximal ideals, and we show that every ideal satisfying the condition C-n is contained in a C-n-maximal ideal. (C) 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of Taibah University.