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Lattice index codes from algebraic number fields [PDF]
2015 IEEE International Symposium on Information Theory (ISIT), 2015 Broadcasting $K$ independent messages to multiple users where each user demands all the messages and has a subset of the messages as side information is studied. Recently, Natarajan, Hong, and Viterbo proposed a novel broadcasting strategy called lattice index coding which uses lattices constructed over some principal ideal domains (PIDs) for ...
Yu-Chih Huang
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Splitting full matrix algebras over algebraic number fields [PDF]
Journal of Algebra, 2012 Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded.
Ivanyos, Gábor +2 more
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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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Factoring Polynomials Over Algebraic Number Fields
ACM Transactions on Mathematical Software, 1976 A method for factoring polynomials whose coefficients are in an algebraic number field is presented. This method is a natural extension of the usual Henselian technique for factoring polynomials with integral coefficients. In addition to working in any number field, our algorithm has the advantage of factoring nonmonic polynomials without inordinately ...
Weinberger, P. J. +1 more
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Universal quadratic forms and indecomposables in number fields: A survey [PDF]
Communications in Mathematics, 2023 We give an overview of universal quadratic forms and lattices, focusing on the recent developments over the rings of integers in totally real number fields. In particular, we discuss indecomposable algebraic integers as one of the main tools.
V. Kala
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Binary forms and orders of algebraic number fields [PDF]
, 1991 Jin Nakagawa
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Gauss Congruences in Algebraic Number Fields
Annales Mathematicae Silesianae, 2022 In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.
Gładki Paweł, Pulikowski Mateusz
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Finiteness theorems for algebraic tori over function fields
Comptes Rendus. Mathématique, 2021 We present a number of finiteness results for algebraic tori (and, more generally, for algebraic groups with toric connected component) over two classes of fields: finitely generated fields and function fields of algebraic varieties over fields of type ...
Rapinchuk, Andrei S., Rapinchuk, Igor A.
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Mathematics, 2021 In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
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