Results 1 to 10 of about 1,992,005 (250)
On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 Let K be an algebraic number field and k be a proper subfield of K. Then we have the relations between the relative degree [K : k] and the increase of the rank of the unit groups.
Itaru Yamaguchi, H. Takeuchi
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A characterization of half-factorial orders in algebraic number fields [PDF]
arXiv, 2023 We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
Balint Rago
arxiv +2 more sources
Improving the efficiency of using multivalued logic tools: application of algebraic rings [PDF]
Scientific Reports, 2023 It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics ...
Ibragim E. Suleimenov +3 more
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Computation of relative integral bases for algebraic number fields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 At first we are given conditions for existence of relative integral bases for extension (K;k)=n. Then we will construct relative integral bases for extensions OK6(−36)/Ok2(−3), OK6(−36)/Ok3(−33), OK6(−36)/Z.
Mahmood Haghighi
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The Genus Field and Genus Number in Algebraic Number Fields [PDF]
Nagoya Mathematical Journal, 1967 Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
Yoshiomi Furuta
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On computing the discriminant of an algebraic number field [PDF]
Mathematics of Computation, 1985 Let f ( x ) f(x) be a monic irreducible polynomial in Z [ x ] {\mathbf {Z}}[x] , and r a root of f ( x ) f(x) in C. Let K be the field Q (
Theresa P. Vaughan
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On the adele rings of algebraic number fields [PDF]
, 1976 Let Q be the rational number field, Q the algebraic closure of Q and k (kaQ) an algebraic number field of finite degree. Let ζk(s) be the Dedekind zeta-function of k, kA the adele ring of k and Gk the Galois group of Q/k with Krull topology.
Keiichi Komatsu
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Fuchsian Groups and Algebraic Number Fields [PDF]
Transactions of the American Mathematical Society, 1985 Given the signature of a finitely-generated Fuchsian group, we find the minimal extension of the rationals for which there is a Fuchsian group having the required signature, whose matrix entries lie in this field.
P. L. Waterman, C. Maclachlan
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Inequalities for ideal bases in algebraic number fields [PDF]
Journal of the Australian Mathematical Society, 1964 K. Mahler
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On the units of an algebraic number field [PDF]
Illinois Journal of Mathematics, 1965 James Ax
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