Abstract
We have shown that the ring A of algebraic integers of an algebraic number field is Noetherian and integrally closed. However, it is not true in general that A is a principal ideal domain.
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© 2001 Springer Science+Business Media New York
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Ribenboim, P. (2001). The Decomposition of Ideals. In: Classical Theory of Algebraic Numbers. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21690-4_7
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DOI: https://doi.org/10.1007/978-0-387-21690-4_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2870-2
Online ISBN: 978-0-387-21690-4
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