Results 221 to 230 of about 1,197 (263)

A design of multiple color image encryption scheme based on finite algebraic structures. [PDF]

Sci Rep
Qayyum T, Shah T, Khan I, Popa IL.
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On cohomology rings of a cyclic group and a ring of integers

On cohomology rings of a cyclic group and a ring of integers
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K2 of rings of algebraic integers

Journal of Number Theory, 1992
For a number field \(F\) and a prime number \(p\), the author studies \(K_ 2{\mathcal O}_ F\otimes\mathbb{Z}_ p\) as a module of Iwasawa descent. The paper consists of two parts: 1) Let \(G_ \infty=\text{Gal}\bigl(F(\mu_{p^ \infty})/F\bigr)\), \(U_ \infty=\) the group of units of \(F\bigl(\mu_{p^ \infty}\bigr)\), \(A_ \infty=\) the \(p\)-class group of
Manfred Kolster
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On cohomology rings of a cyclic group and a ring of integers

SUT Journal of Mathematics, 2002
Let \(p\) be a prime number, \(G\) be the cyclic group of order \(p^\nu\), \(\nu\) a positive integer \(\geq 1\), and \(\Gamma\) be the ring of integers of the cyclotomic field \(\mathbb{Q}(\zeta)\) for a primitive \(p^\nu\)-th root of unity \(\zeta\).
Hayami, Takao, Sanada, Katsunori
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P-adic Approximation of Algebraic Integers and Residue Class Rings of Rings of Integer-Valued Polynomials

Springer Proceedings in Mathematics and Statistics
Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series ...
Sophie Frisch, Franz Halter-Koch
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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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Sum of Divisors in a Ring of Gaussian Integers

Ukrainian Mathematical Journal, 2001
Summary: We construct an asymptotic formula for a summation function for \(\sigma_a(\alpha)\), where \(\sigma_a(\alpha)\) is the sum of the \(a\)-th powers of the norms of divisors of the Gaussian integer \(\alpha\) on an arithmetic progression \(\alpha\sim\alpha_0\pmod\gamma\) and in a narrow sector \(\phi_1\leq\operatorname {arg ...
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Multiplication Of Polynomials Over The Ring Of Integers

25th Annual Symposium onFoundations of Computer Science, 1984., 2005
Let R be a ring, and let f(/spl alpha/), g(/spl alph/) /spl epsi/ R[/spl alpha/] be univariate polynomials over R of degree n. We Present an algorithm for computing the coefficients of the product f(/spl alpha/)G (/spl alpha/) by O (nlgn) multiplications. This algorithm is based on an algorithm for multiplying polynomials over the ring of integers, and
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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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