For an integral domain D, the irreducible divisor graph G D (x) of a nonunit x ∈ D gives a visual representation of the factorizations of x. Here we consider a higher-dimensional generalization of this notion, the irreducible divisor simplicial complex S D (x). We show how this new structure is a true generalization of G D (x), and show that it often carries more information about the element x and the domain D than its two-dimensional counterpart.
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