Results 131 to 140 of about 11,330 (177)

Cyclotomic Splitting Fields

Canadian Mathematical Bulletin, 1982
AbstractLet D be a division algebra whose class [D] is in B(K), the Brauer group of an algebraic number field K. If [D⊗KL] is the trivial class in B(L), then we say that L is a splitting field for D or L splits D. The splitting fields in D of smallest dimension are the maximal subfields of D.
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MONOGENEITY IN CYCLOTOMIC FIELDS

International Journal of Number Theory, 2010
A number field is said to be monogenic if its ring of integers is a simple ring extension ℤ[α] of ℤ. It is a classical and usually difficult problem to determine whether a given number field is monogenic and, if it is, to find all numbers α that generate a power integral basis {1, α, α2, …, αk} for the ring.
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CYCLOTOMIC FIELDS AND MODULAR CURVES

Russian Mathematical Surveys, 1971
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The cyclotomic fields

2021
IV SAYKLOTOMİK ALANLARDAKİ L-FONKSIYONLARI İsmail KOCAMEŞE Yüksek Lisans Tezi - Matematik Ocak 2005 Tez Yöneticisi: Prof. Dr. Barış KENDİRLİ ÖZ Bu çalışmada Dirihlet L-fonksiyonları ele alınmıştır. Bunun yanı sıra, sayklotomik alanlar çalışılmıştır. Ayrıca, genel L-fonksiyonları ve saylotomik alanlardaki L-fonksiyonları çalışılmıştır. Anahtar Kelimeler:
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Quadratic-Residue Codes and Cyclotomic Fields

Acta Applicandae Mathematicae, 2006
The authors look at cyclic codes of prime length \(p\) over a field a Galois field \(\text{GF}(q)\) where \(q\) is a prime that is a quadratic residue modulo \(p\). They do so via their embedding in codes over the quadratic field \(\mathbb Q(\sqrt{(-1)^{(p-1)/2}p})\).
ELIA, Michele, J. CARMELO INTERLANDO
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Regular Cyclotomic Fields

1998
Let l be an odd prime number and k (ζ) the cyclotomic field generated by = ζ = e 2πi/l is called a regular cyclotomic field and l is called a regular prime number if the number of ideal classes of the field k (ζ) is not divisible by l. The remaining chapters will be concerned exclusively with regular cyclotomic fields and with Kummer fields derived ...
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Cyclotomic Number Fields

2000
This chapter is devoted to some proofs of the quadratic reciprocity law that make use of the arithmetic of cyclotomic number fields.
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Cyclotomic Function Fields

2002
In the last chapter we explored the arithmetic of constant field extensions and noted (as was pointed out by Iwasawa) that these extensions can be thought of as function field analogues of cyclotomic extensions of number fields. This analogy led to various conjectures about the behavior of class groups in number fields which have proved very fruitful ...
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Quadratic and Cyclotomic Fields

1982
In the last chapter we discussed the general theory of algebraic number fields and their rings of integers. We now consider in greater detail two important classes of these fields which were studied first in the nineteenth century by Gauss, Eisenstein, Kummer, Dirichlet, and others in connection with the theory of quadratic forms, higher reciprocity ...
Kenneth Ireland, Michael Rosen
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Cyclotomic Fields as Abelian Fields

1998
For each positive integer m the cyclotomic field of the m-th roots of unity is easily seen to be an abelian field and indeed we have the following more detailed results.
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