Faster access than browser!
29 relations: Ascending chain condition on principal ideals, Bézout's identity, Carl Friedrich Gauss, Commutative ring, Composite number, Congruence (geometry), Coprime integers, Disquisitiones Arithmeticae, Euclid, Euclid's Elements, Euclidean algorithm, Fundamental theorem of arithmetic, Gauss's lemma (number theory), Integral domain, Irreducible element, Jean Prestet, Lemma (mathematics), Logical equivalence, Mathematical induction, Number theory, Oxford University Press, Prime element, Prime number, Q.E.D., Solution of triangles, Springer Science+Business Media, Triangle, Undergraduate Texts in Mathematics, Unique factorization domain.
Ascending chain condition on principal ideals
In abstract algebra, the ascending chain condition can be applied to the posets of principal left, principal right, or principal two-sided ideals of a ring, partially ordered by inclusion.
New!!: Euclid's lemma and Ascending chain condition on principal ideals · See more »
Bézout's identity
In elementary number theory, Bézout's identity (also called Bézout's lemma) is the following theorem: The integers x and y are called Bézout coefficients for (a, b); they are not unique.
New!!: Euclid's lemma and Bézout's identity · See more »
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
New!!: Euclid's lemma and Carl Friedrich Gauss · See more »
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
New!!: Euclid's lemma and Commutative ring · See more »
Composite number
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.
New!!: Euclid's lemma and Composite number · See more »
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
New!!: Euclid's lemma and Congruence (geometry) · See more »
Coprime integers
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
New!!: Euclid's lemma and Coprime integers · See more »
Disquisitiones Arithmeticae
The Disquisitiones Arithmeticae (Latin for "Arithmetical Investigations") is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24.
New!!: Euclid's lemma and Disquisitiones Arithmeticae · See more »
Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
New!!: Euclid's lemma and Euclid · See more »
Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
New!!: Euclid's lemma and Euclid's Elements · See more »
Euclidean algorithm
. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.
New!!: Euclid's lemma and Euclidean algorithm · See more »
Fundamental theorem of arithmetic
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.
New!!: Euclid's lemma and Fundamental theorem of arithmetic · See more »
Gauss's lemma (number theory)
Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue.
New!!: Euclid's lemma and Gauss's lemma (number theory) · See more »
Integral domain
In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
New!!: Euclid's lemma and Integral domain · See more »
Irreducible element
In abstract algebra, a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units.
New!!: Euclid's lemma and Irreducible element · See more »
Jean Prestet
Jean Prestet (1648–1691) was a French Oratorian priest and mathematician who contributed to the fields of combinatorics and number theory.
New!!: Euclid's lemma and Jean Prestet · See more »
Lemma (mathematics)
In mathematics, a "helping theorem" or lemma (plural lemmas or lemmata) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.
New!!: Euclid's lemma and Lemma (mathematics) · See more »
Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.
New!!: Euclid's lemma and Logical equivalence · See more »
Mathematical induction
Mathematical induction is a mathematical proof technique.
New!!: Euclid's lemma and Mathematical induction · See more »
Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
New!!: Euclid's lemma and Number theory · See more »
Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
New!!: Euclid's lemma and Oxford University Press · See more »
Prime element
In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polynomials.
New!!: Euclid's lemma and Prime element · See more »
Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
New!!: Euclid's lemma and Prime number · See more »
Q.E.D.
Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.
New!!: Euclid's lemma and Q.E.D. · See more »
Solution of triangles
Solution of triangles (solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known.
New!!: Euclid's lemma and Solution of triangles · See more »
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
New!!: Euclid's lemma and Springer Science+Business Media · See more »
Triangle
A triangle is a polygon with three edges and three vertices.
New!!: Euclid's lemma and Triangle · See more »
Undergraduate Texts in Mathematics
Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag.
New!!: Euclid's lemma and Undergraduate Texts in Mathematics · See more »
Unique factorization domain
In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.
New!!: Euclid's lemma and Unique factorization domain · See more »
Redirects here:
Euclid lemma, Euclid's first theorem, Euclid's lemma proof.
References
[1] https://en.wikipedia.org/wiki/Euclid's_lemma
