Results 211 to 220 of about 379,338 (251)
Lorentzian bordisms in algebraic quantum field theory. [PDF]
Lett Math PhysBunk S, MacManus J, Schenkel A.
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Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids. [PDF]
Sci RepSingh K, Varghese SS, Kourakis I.
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Journal of Soviet Mathematics, 1987
Translation from Itogi Nauki Tekh., Ser. Algebra Topol. Geom. 22, 117--204 (Russian) (1984; Zbl 0563.12002).
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Translation from Itogi Nauki Tekh., Ser. Algebra Topol. Geom. 22, 117--204 (Russian) (1984; Zbl 0563.12002).
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1967
We shall need some elementary results about vector-spaces over Q, involving the following concept: Definition 1. Let E be a vector-space of finite dimension over Q. By a Q-lattice in E, we understand a finitely generated subgroup of E which contains a basis of E over Q. Proposition 1.
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We shall need some elementary results about vector-spaces over Q, involving the following concept: Definition 1. Let E be a vector-space of finite dimension over Q. By a Q-lattice in E, we understand a finitely generated subgroup of E which contains a basis of E over Q. Proposition 1.
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On number systems in algebraic number fields
Publicationes Mathematicae Debrecen, 1992Let \(\theta\) be an algebraic integer over \(\mathbb{Q}\) and \(A\subset \mathbb{Z}[\theta]\) be a complete residue system \(\text{mod } \theta\). The authors consider expansions of the elements \(\alpha\in \mathbb{Z}[\theta]\) in powers of \(\theta\) with coefficients \(\alpha_ k\in A\) defined by \(\alpha_ k= \alpha_{k+1}\theta+b_ k\), where \(b_ k ...
Kátai, I., Környei, I.
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2012
This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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Realizing Algebraic Number Fields
1983In the paper [13], the authors studied the problem of realizing rational division algebras in a special way. Let D be a division algebra that is finite dimensional over the rational field Q. If p is a prime, we say that D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is ...
R. S. Pierce, C. I. Vinsonhaler
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2019
A complex number \(\xi \) is called an algebraic integer if \(\mathbf {Z}[ \xi ]\) is a finitely generated \(\mathbf {Z}\)-module; this condition is equivalent to the fact that \(f( \xi )=0\) for some polynomial \(f(X)=X^m+a_1X^{m-1}+ \cdots +a_m\), \(a_i \in \mathbf {Z}\). Let \(\mathbf {A}\) be the set of all algebraic integers.
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A complex number \(\xi \) is called an algebraic integer if \(\mathbf {Z}[ \xi ]\) is a finitely generated \(\mathbf {Z}\)-module; this condition is equivalent to the fact that \(f( \xi )=0\) for some polynomial \(f(X)=X^m+a_1X^{m-1}+ \cdots +a_m\), \(a_i \in \mathbf {Z}\). Let \(\mathbf {A}\) be the set of all algebraic integers.
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1981
A system of complex numbers is called a number field (or, more briefly, a field) if it contains more than one number and if along with the numbers α and β it always contains α + β, α − β,αβ, and, if β ≠ 0, α/β.
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A system of complex numbers is called a number field (or, more briefly, a field) if it contains more than one number and if along with the numbers α and β it always contains α + β, α − β,αβ, and, if β ≠ 0, α/β.
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