Transfinitely valued Euclidean domains have arbitrary indecomposable order type |
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| Authors: | Chris J Conidis Vandy Tombs |
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| Institution: | 1. Department of Mathematics, College of Staten Island, The City University of New York, New York, NY, USA;2. Department of Mathematics, Brigham Young University, Provo, UT, USA |
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| Abstract: | We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely characterize the norm complexity of Euclidean domains. Modifying this construction, we also find a finitely valued Euclidean domain with no multiplicative integer valued norm. |
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| Keywords: | Euclidean domain indecomposable ordinal multiplicative norm transfinitely valued |
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