The Prime Ideal Factorization of 2 in Pure Quartic Fields with Index 2
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Abstract
The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicitly. Let K be an algebraic number field and OK its ring of integers. When determining generators of the ideals in the prime ideal factorization of a (rational) prime p in OK, the most difficult case occurs when p divides the field index i(K) of K. In this paper we examine the case when K is a pure quartic field. Here i(K) = 1 or 2, and we determine explicit generators of the prime ideals in the decomposition of 2 when i(K) = 2. Let K be a pure quartic field. Then there exists a fourth power free integer m such that K = Q(m 1/4 ). It follows from the work of Funakura (1,
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
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