Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of Q [PDF]
Annals of Pure and Applied Logic, 1994 This paper provides the first examples of rings of algebraic numbers containing the rings of algebraic integers of the infinite algebraic extensions of Q, where Hilbert’s Tenth Problem is undecidable.
Alexandra Shlapentokh
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Hybrid structure of maximal ideals in near rings [PDF]
Complex & Intelligent SystemsA hybrid structure is an arrangement that makes use of many hierarchical reporting structures and is applied to algebraic structures such as groups and rings.
B. Jebapresitha
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A Diophantine definition of rational integers over some rings of algebraic numbers. [PDF]
Notre Dame Journal of Formal Logic, 1992 After a negative answer was given to Hilbert's Tenth Problem (that is, is there an algorithm that identifies the diophantine equations which have rational integer solutions and those that don't?) it is natural to ask a similar question in various other domains, for example, in the ring of integers \({\mathcal O}_ K\) of a number field \(K\).
Alexandra Shlapentokh
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Frieze patterns over algebraic numbers [PDF]
Bulletin of the London Mathematical Society, 2023 Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jørgensen ...
M. Cuntz, T. Holm, Carlo Pagano
semanticscholar +4 more sources
Phase Transitions on C*-Algebras from Actions of Congruence Monoids on Rings of Algebraic Integers [PDF]
International mathematics research notices, 2019 We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers.
Chris Bruce
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Wave Transport and Localization in Prime Number Landscapes
Frontiers in Physics, 2021 In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields.
Luca Dal Negro +4 more
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On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field [PDF]
Proceedings of the American Mathematical Society, 1969 On the basis of these results he conjectured in [9] that the groups Hr(G, OF) have the same order also in the case when G is not cyclic. In the present note, we shall show that the conjecture is false. We shall also demonstrate how the problem of determining Hr(G, OF) can be localized.
Lee, M. P., Madan, M. L.
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Two-primary algebraic 𝐾-theory of rings of integers in number fields [PDF]
Journal of the American Mathematical Society, 1999 We relate the algebraic K K -theory of the ring of integers in a number field
J. Rognes +2 more
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Algorithmic search for integer Abelian roots of a polynomial with integer Abelian coefficients [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаIn this work, we consider the operations over Abelian integers of rank $n$. By definition, such numbers are elements of the complex field and have the form of polynomials with integer coefficients from the $n$th degree primitive root of 1.
Tsybulya, Liliya Mikhailovna
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On the integer ring of the compositum of algebraic number fields [PDF]
Nagoya Mathematical Journal, 1980 Let k be an algebraic number field of finite degree. For a finite extension L/k we denote by L/k the different of L/k, and by L the integer ring of L. Let K1 and K2 be finite extensions of k.
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