Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a which allows a suitable generalization of the Euclidean division of the integers. This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them (Bézout's identity). Also every ideal in a Euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic: every Euclidean domain is a unique fact
Algebraic number fieldBerlekamp's algorithmCantor–Zassenhaus algorithmChinese remainder theoremConway polyhedron notationCubic reciprocityDedekind–Hasse normDegree of a polynomialDiscrete valuation ringDivision (mathematics)DomainEisenstein integerEuclideanEuclidean algorithmEuclidean divisionEuclidean functionEuclidean ringEuclidean valuationEuclidian domainExtended Euclidean algorithmFactorizationFormal derivativeFundamental polygonFundamental theorem of arithmeticGaussian integerGlossary of commutative algebraGoldberg–Coxeter constructionGreatest common divisorIdeal class groupIntegerLagrange's four-square theoremList of abstract algebra topicsList of commutative algebra topicsList of things named after EuclidNoetherian ringNormNorm-Euclidean fieldOrdinal arithmeticPolynomialPolynomial greatest common divisor
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Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a which allows a suitable generalization of the Euclidean division of the integers. This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them (Bézout's identity). Also every ideal in a Euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic: every Euclidean domain is a unique fact
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Dziedzina Euklidesa (albo pier ...... za pomocą algorytmu Euklidesa.
@pl
Em álgebra abstrata, um domíni ...... mo de Euclides pode ser usado.
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En matemáticas, más concretame ...... minio de factorización única.
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En mathématiques et plus préci ...... ne arithmétique des polynômes.
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Ett euklidiskt område eller eu ...... män och varje element har en .
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Eukleidovský obor (nebo euklei ...... o společného dělitele hledáme.
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In algebra, un dominio euclide ...... ttuare una divisione euclidea.
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In de abstracte algebra en de ...... ⊂ commutatieve ringen ⊂ ringen
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In der Mathematik ist ein eukl ...... urch eine geeignete definiert.
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In mathematics, more specifica ...... ⊃ algebraically closed fields
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Dziedzina Euklidesa (albo pier ...... za pomocą algorytmu Euklidesa.
@pl
Em álgebra abstrata, um domíni ...... mo de Euclides pode ser usado.
@pt
En matemáticas, más concretame ...... n lineal de ellos (identidad d
@es
En mathématiques et plus préci ...... inir une division euclidienne.
@fr
Ett euklidiskt område eller eu ...... män och varje element har en .
@sv
Eukleidovský obor (nebo euklei ...... i v některých jiných okruzích.
@cs
In algebra, un dominio euclide ...... ttuare una divisione euclidea.
@it
In de abstracte algebra en de ...... ⊂ commutatieve ringen ⊂ ringen
@nl
In der Mathematik ist ein eukl ...... urch eine geeignete definiert.
@de
In mathematics, more specifica ...... lidean domain is a unique fact
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label
Anell euclidià
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Anneau euclidien
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Dominio euclideo
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Dominio euclídeo
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Domínio euclidiano
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Dziedzina Euklidesa
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Euclidean domain
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Euclidisch domein
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Eukleidovský obor
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Euklidischer Ring
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