Irreducible Divisor Simplicial Complexes
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Recently there has been much research on irreducible divisor graphs | visual representations of the factorizations of elements in commutative rings. In this thesis we expand on this concept by introducing the irreducible divisor simplicial complex of an element in an integral domain, e ffectively constructing a higher dimensional analog of the irreducible divisor graph. We show that this new construction often sheds more light on the factorization of elements than its two-dimensional counterpart. In addition, we generalize several important irreducible divisor graph results.