Results 21 to 30 of about 10,375,970 (302)
Improving the efficiency of using multivalued logic tools: application of algebraic rings
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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Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
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Upper bounds for Euclidean minima of algebraic number fields [PDF]
, 2006 The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor ...
Bayer Fluckiger, Eva
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Quadratic forms and linear algebraic groups [PDF]
, 2009 Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties ...
Harbater, David +3 more
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Machine-learning number fields
, 2022 We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is trained on finitely many Dedekind zeta coefficients is able to distinguish ...
Oliver, T., He, Y.-H., Lee, K.-H.
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Computation of the Euclidean minimum of algebraic number fields [PDF]
, 2014 30 pages, shorter version, with many typos fixedInternational audienceWe present an algorithm to compute the Euclidean minimum of an algebraic number field, which is a generalization of the algorithm restricted to the totally real case described by Cerri.
Pierre Lezowski, Lezowski, Pierre
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On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 Let \(K\) be an algebraic number field of degree \(n\) over the rational number field and \(k\) be a proper subfield of \(K\) with \([K: k]=m\). Further, let \(R_ 1\), \(r_ 1\) denote the number of embeddings of \(K\), \(k\) into the real numbers and \(2R_ 2\), \(2r_ 2\) denote the numbers of embeddings of \(K\), \(k\) into the complex numbers.
Yamaguchi, I., Takeuchi, H.
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Relative integral basis for algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 1986 At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(m3).
Mohmood Haghighi
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Units in families of totally complex algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 2004 Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number ...
L. Ya. Vulakh
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A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)
Trends in Computational and Applied Mathematics, 2019 The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of ...
Antonio A. Andrade +2 more
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