Abstract
In this chapter, we begin the study of extensions of ideals. Let K be an algebraic number field, let L⃒K be an extension of finite degree, and let A (respectively, B), be the rings of algebraic integers of K (respectively, L). Let I be any nonzero fractional ideal of K. The aim of this study is to relate the decomposition of I into prime ideals of A, with the decomposition into prime ideals of B, of the fractional ideal of L generated by I.
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© 2001 Springer Science+Business Media New York
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Ribenboim, P. (2001). Extension of Ideals. In: Classical Theory of Algebraic Numbers. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21690-4_11
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DOI: https://doi.org/10.1007/978-0-387-21690-4_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2870-2
Online ISBN: 978-0-387-21690-4
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