Results 11 to 20 of about 9,944 (204)
Pythagoras numbers for infinite algebraic fields [PDF]
Revista Matemática ComplutenseWe prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic
Nicolas Daans +3 more
semanticscholar +3 more sources
Certifying Rings of Integers in Number Fields [PDF]
Certified Programs and ProofsNumber fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects of these.
Anne Baanen +2 more
semanticscholar +3 more sources
A formal proof of Hensel's lemma over the p-adic integers [PDF]
Certified Programs and Proofs, 2019 The field of p-adic numbers ℚp and the ring of p-adic integers ℤp are essential constructions of modern number theory. Hensel’s lemma, described by Gouvêa as the “most important algebraic property of the p-adic numbers,” shows the existence of roots of ...
R. Lewis
semanticscholar +5 more sources
Elliptic curves retaining their rank in finite extensions and Hilbert’s Tenth Problem for rings of algebraic numbers [PDF]
, 2008 Using Poonen's version of the "weak vertical method" we produce new examples of "large" and "small" rings of algebraic numbers (including rings of integers) where Z and/or the ring of integers of a subfield are existentially definable and/or where the ...
Alexandra Shlapentokh
semanticscholar +2 more sources
Euclidean Rings of Algebraic Integers [PDF]
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2004 Let K be a finite Galois extension of the field of rational numbers with unit rank greater than 3. We prove that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption
Malcolm Harper, M. Murty
semanticscholar +2 more sources
Carmichael numbers in number rings [PDF]
, 2008 We generalize Carmichael numbers to ideals in number rings and prove a generalization of Korselt's Criterion for these Carmichael ideals. We investigate when Carmichael numbers in the integers generate Carmichael ideals in the algebraic integers of ...
G. Steele
semanticscholar +2 more sources
Other Structures of Rings of Integers Numbers, Isomorphic Between Them
, 2020 As it is known, often solving a problem in a certain algebraic structure is quite difficult. That is why it is sometimes necessary to transfer the problem in an isomorphic structure with the given one and where it can be solved more easily.
Teodor-Dumitru Vălcan
semanticscholar +1 more source
Factor equivalence of Galois modules and regulator constants [PDF]
, 2013 We compare two approaches to the study of Galois module structures: on the one hand, factor equivalence, a technique that has been used by Fröhlich and others to investigate the Galois module structure of rings of integers of number fields and of their ...
Bartel, Alex, Alex Bartel
core +1 more source
On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group [PDF]
Nagoya Mathematical Journal, 1960 1. Introduction. It is known that there are only three rationally inequivalent classes of indecomposable integral representations of a cyclic group of prime order l. The representations of these classes are: (I) identical representation,(II) rationally irreducible representation of degree l – 1,(III) indecomposable representation consisting of one ...
openaire +3 more sources
Adaptive compute-and-forward with lattice codes over algebraic integers [PDF]
International Symposium on Information Theory, 2015 We consider the compute-and-forward relay network with limited feedback. A novel scheme called adaptive compute-and-forward is proposed to exploit the channel knowledge by working with the best ring of imaginary quadratic integers.
Yu-Chih Huang +2 more
semanticscholar +1 more source