Results 31 to 40 of about 131,023 (367)
Approximatting rings of integers in number fields [PDF]
Journal de théorie des nombres de Bordeaux, 1994 In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be well-solved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients.
Lenstra, H.W., Buchmann, J.A.
openaire +2 more sources
The Fourier restriction and Kakeya problems over rings of integers modulo N [PDF]
Discrete Analysis, 2018 The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting of the ring of integers modulo $N$ for general $N$ and a striking similarity with the corresponding euclidean problems is observed.
Jonathan Hickman, James Wright
openalex +3 more sources
A universal first order formula defining the ring of integers in a number field [PDF]
, 2012 We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ..., x_N) is not 0}.
Jennifer Park
semanticscholar +1 more source
Известия Иркутского государственного университета: Серия "Математика", 2022 M. C. Tamburini and P. Zucca proved that the special linear group of dimension greater than 13 over the ring of Gaussian integers is generated by three involutions, two of which commute (J. of Algebra, 1997).
R. I. Gvozdev +2 more
doaj +1 more source
Polynomial multiple recurrence over rings of integers [PDF]
Ergodic Theory and Dynamical Systems, 2015 We generalize the polynomial Szemerédi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of $\mathbb{Z}^{m}$ and strengthens and extends recent results ...
Robertson, Donald, Bergelson, Vitaly
openaire +3 more sources
Sums of units in function fields II - The extension problem [PDF]
, 2013 In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)?
Frei, Christopher
core +1 more source
Geometric configurations in the ring of integers modulo $p^{\ell}$ [PDF]
, 2011 We study variants of the Erd\H os distance problem and dot products problem in the setting of the integers modulo $q$, where $q = p^{\ell}$ is a power of an odd prime.
D. Covert +2 more
semanticscholar +1 more source
Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings
Neutrosophic Sets and Systems, 2018 The concept of neutrosophy and indeterminacy I was introduced by Smarandache, to deal with neutralies. Since then the notions of neutrosophic rings, neutrosophic semigroups and other algebraic structures have been developed.
Vasantha W.B +2 more
doaj +1 more source
Trivial units for group rings over rings of algebraic integers [PDF]
Proceedings of the American Mathematical Society, 2005 Let G G be a nontrivial torsion group and R R be the ring of integers of an algebraic number field. The necessary and sufficient conditions are given under which R G RG has only trivial units.
Herman, Allen, Li, Yuanlin
openaire +1 more source
Endomorphisms and Product Bases of the Baer-Specker Group
International Journal of Mathematics and Mathematical Sciences, 2009 The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers.
E. F. Cornelius
doaj +1 more source