Results 11 to 20 of about 165,977,654 (290)

Gaussian Integers and Other Quadratic Integer Rings

, 2021
This thesis deals with quadratic integer rings, in particular the Gaussian integers Z}[i]. Concepts such as quadratic extensions, Euclidean domains and unique factorization domains will be introduced to the reader. The goal of this thesis is to show how a natural generalization of the integers Z, in the form of the Gaussian integers, can be used to ...
Landin, Erik, Hussein, Seif
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Primitive near-rings [PDF]

, 1970
The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms.
Holcombe, William Michael Lloyd
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Gauss Congruences in Algebraic Number Fields

Annales Mathematicae Silesianae, 2022
In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.
Gładki Paweł, Pulikowski Mateusz
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Enumeration of Involutions of Finite Rings

Journal of New Theory, 2021
In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R.
Sajana Shaık, Chalapathi Tekurı
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On The Symbolic 2-Plithogenic Number Theory and Integers [PDF]

Neutrosophic Sets and Systems, 2023
The objective of this paper is to study for the first time the foundational concepts of number theory in 2-plithogenic rings of integers, where concepts such as symbolic 2-plithogenic congruencies, division, semi primes, and greatest common divisors.
Hamiyet Merkepci, Ammar Rawashdeh
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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
openaire   +4 more sources

Characterizations of rings and modules by means of lattices [PDF]

, 1965
PhDIn this thesis we study the relationship between the lattice of submodules and the algebraic structure of a module. The key remark in our study will be the fact that the homomorphisms between two independent submadules of a module can be ...
Stephenson, W.
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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
openaire   +2 more sources

"Exotic" binary number systems for rings of Gauss and Eisenstein integers [PDF]

Компьютерная оптика, 2018
The paper considers nonstandard binary number systems for rings of Gauss and Eisenstein integers. The principal difference ("exoticism") of such number systems from the canonical number systems introduced by I.
Vladimir Chernov
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Implicit linear difference equations over a non-Archi-medean ring

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021
Over any field an implicit linear difference equation one can reduce to the usual explicit one, which has infinitely many solutions ~ one for each initial value.
Anna Goncharuk
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