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Placido Sub-Pixel Edge Detection Algorithm Based on Enhanced Mexican Hat Wavelet Transform and Improved Zernike Moments. [PDF]
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Representations of Cyclic Groups in Rings of Integers, I
The Annals of Mathematics, 1962Let 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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Rings: Applications of the integers
1976In 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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Similarity of matrices with integer spectrum over the ring of integers
Russian Mathematics, 2011For matrices with integer elements which have the same integer spectrum and whose Jordan form contains no blocks of the same order for one and the same eigenvalue, we propose a quasipolynomial-time algorithm for recognizing their similarity over the ring of integers.
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UNDECIDABILITY OF FAMILIES OF RINGS OF TOTALLY REAL INTEGERS
International Journal of Number Theory, 2008Let 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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A CONSTRUCTION OF THE RING OF INTEGERS
JP Journal of Algebra, Number Theory and Applications, 2020Cherniavsky, Yonah, Jarden, Adi
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