Results 21 to 30 of about 114,538 (286)
Computing in quotients of rings of integers [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractWe develop algorithms to turn quotients of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavior under certain quotients.
Claus Fieker, Tommy Hofmann
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Euclidean Rings of Algebraic Integers [PDF]
Canadian Journal of Mathematics, 2004 AbstractLet 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 of the generalized Riemann hypothesis for Dedekind zeta functions.
Harper, Malcolm, Murty, M. Ram
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∗-Regularity in the ring of matrices over the ring of integers modulo 𝑛 [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 For any positive integer 𝑛 ≥ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo 𝑛.
Wannisa Apairat, Sompong Chuysurichay
doaj
The étale cohomology ring of the ring of integers of a number field
Research in Number Theory, 2023 AbstractWe compute the cohomology ring $$H^*(X,{{\mathbb {Z}}}/n{{\mathbb {Z}}})$$ H ∗ ( X , Z /
Eric Ahlqvist, Magnus Carlson
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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
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Vector Bundles on the Moduli Stack of Elliptic Curves [PDF]
, 2015 We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles.
Bauer +28 more
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Polyadic rings of p-adic integers
Symmetry, 2022 In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become $\left( m,n\right) $-rings. Second, we introduce a possible $p$-adic analog of the residue class modulo a $p$-adic integer. Then, we find the relations which determine, when the representatives form a $\left( m,n\right) $-ring.
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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
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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.
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Nondefinability of Rings of Integers in Most Algebraic Fields [PDF]
Notre Dame Journal of Formal Logic, 2021 We show that the set of algebraic extensions $F$ of $\mathbb{Q}$ in which $\mathbb{Z}$ or the ring of integers $\mathcal{O}_F$ are definable is meager in the set of all algebraic extensions.
Philip Dittmann, Arno Fehm
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