Elsevier BV Acta Medica Okayama 0022-4049 226 8 2022 Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring 107026 EN Futoshi Hayasaka Department of Environmental and Mathematical Sciences, Okayama University In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and numerical results on integrally closed modules. These are used in the proof of indecomposability of the modules. As a consequence, we have a large class of indecomposable integrally closed modules of arbitrary rank whose ideal is not necessarily simple. This extends the original result on the existence of indecomposable integrally closed modules and strengthens the non-triviality of the theory developed by Kodiyalam. No potential conflict of interest relevant to this article was reported.

Academic Press Acta Medica Okayama 00218693 556 2020 Constructing indecomposable integrally closed modules over a two-dimensional regular local ring 879 907 EN Futoshi Hayasaka Department of Environmental and Mathematical Sciences, Okayama University In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question. No potential conflict of interest relevant to this article was reported.