Results 321 to 330 of about 131,023 (367)

Representations of Cyclic Groups in Rings of Integers, I

The Annals of Mathematics, 1962
Let Gk be a cyclic group of order k, and let ZGk denote its group ring over the ring Z of rational integers. We denote by n(ZGk) the number of non-isomorphic indecomposable left ZGk-modules having finite Z-bases. In 1938 Diederichsen [2] proved that n(ZG,) is finite for p a rational prime, and gave an incorrect proof that n(ZG4) is infinite.
Heller, A., Reiner, Irving
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The Ring of Integers Modulo n

2008
W. Stein
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Towards Hilbert’s tenth problem for rings of integers through Iwasawa theory and Heegner points

Mathematische Annalen, 2019
For a positive proportion of primes p and q , we prove that $${\mathbb {Z}}$$ Z is Diophantine in the ring of integers of $${\mathbb {Q}}(\root 3 \of {p},\sqrt{-q})$$ Q ( p 3 , - q ) .
N. Garcia-Fritz, Hector Pasten
semanticscholar   +1 more source

Universality of certain diagonal quadratic forms for matrices over a ring of integers

Indian journal of pure and applied mathematics, 2022
Murtuza Nullwala, Anuradha S. Garge
semanticscholar   +1 more source

Rings: Applications of the integers

1976
In this chapter we assemble some results on rings which we obtain by using a specific knowledge of the natural numbers and the integers. We begin the chapter with some work refining our knowledge of finite and infinite sets. We then routinely study some theorems extending the associative, commutative, and distributive laws to any finite number of ...
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Some aspects of zero-divisor graphs for the ring of Gaussian integers modulo $$2^{n}$$ 2 n

Journal of Applied Mathematics and Computation, 2021
Deepa Sinha, Bableen Kaur
semanticscholar   +1 more source

UNDECIDABILITY OF FAMILIES OF RINGS OF TOTALLY REAL INTEGERS

International Journal of Number Theory, 2008
Let ℤtrbe the ring of totally real integers, Gal(ℚ) the absolute Galois group of ℚ, and e a positive integer. For each σ = (σ1,…,σe) ∈ Gal (ℚ)elet ℤtr(σ) be the fixed ring in ℤtrof σ1,…,σe. Then, the theory of all first order sentences θ that are true in ℤtr(σ) for almost all σ ∈ Gal (ℚ)e(in the sense of the Haar measure) is undecidable.
Jarden, Moshe, Videla, Carlos R.
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Explicit Polynomial Generators for the Ring of Quasisymmetric Functions over the Integers

, 2004
In (Hazewinkel in Adv. Math. 164:283–300, 2001, and CWI preprint, 2001) it has been proved that the ring of quasisymmetric functions over the integers is free polynomial.
M. Hazewinkel
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Catalytic Enantioselective Ring-Opening Reactions of Cyclopropanes

Chemical Reviews, 2021
Vincent Pirenne, Bastian Muriel, Jerome Waser   +2 more
exaly  

Factor Rings of Integers

The American Mathematical Monthly, 1989
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