Results 11 to 20 of about 268,040 (278)
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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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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Lower bounds on the class number of algebraic function fields defined over any finite field [PDF]
, 2011 We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field.
Ballet, Stéphane, Rolland, Robert
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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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Right triangles with algebraic sides and elliptic curves over number fields [PDF]
, 2009 Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem.
Girondo, Ernesto +4 more
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A Topological Perspective on Interacting Algebraic Theories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum computation.
Amar Hadzihasanovic
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Algorithms in algebraic number theory [PDF]
, 1992 In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and,
Lenstra Jr., Hendrik W.
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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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On some varieties associated with trees [PDF]
, 2014 This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be smooth and to
Chapoton, Frédéric
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