Abstract

For a large class of purely infinite right self-injective regular rings, wedescribe the lattice of two-sided ideals as a lattice of ideals of a certain lattice of continuous functions. For rings of type I or II, our result is a generalization of the corresponding one in the prime case obtained by Goodearl. The main tools that we use are the relative and infinite Goodearl-Boyle dimension functions. These functions are glued together in order to obtain a dimension function D defined on the lattice of principal right ideals. The computation of the range of D constitutes the key point in proving our main result.

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