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In this paper, we construct indecomposable integrally closed modules ofarbitrary rank over a two-dimensional regular local ring. The modules are quiteexplicitly constructed from a given complete monomial ideal. We also givestructural and numerical results on integrally closed modules. These are usedin the proof of indecomposability of the modules. As a consequence, we have alarge class of indecomposable integrally closed modules of arbitrary rank whoseideal is not necessarily simple. This extends the original result on theexistence of indecomposable integrally closed modules and strengthens thenon-triviality of the theory developed by Kodiyalam.

Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring