Maximal common divisor information

particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is...

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of...

the concept of a maximal common divisor is needed to generalize greatest common divisors to number systems in which the common divisors of a set of elements...

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor...

having zero divisors. The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block...

the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity...

common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors,...

N(d) of the greatest common divisor of a and b is a common divisor of N(a), N(b), and N(a + b). When the greatest common divisor D of these three integers...

division with remainder, for example, Euclid's algorithm for the greatest common divisor. Gaussian integer Eisenstein integer The icosians The Lie group F4 The...

to the set of its prime divisors. It is order-preserving: if x divides y, then each prime divisor of x is also a prime divisor of y. However, it is neither...

span, set by the numbers with 7 and 11 divisors, and followed by numbers with 13 and 17 divisors; these are maximal records set by successive prime counts...

of f, and the greatest common divisor of two polynomials is independent of the ambient field, so the greatest common divisor of f and f′ has coefficients...

polynomial with integer coefficients that is a divisor of x n − 1 {\displaystyle x^{n}-1} and is not a divisor of x k − 1 {\displaystyle x^{k}-1} for any...

zero-divisors and where 1≠0. dominate A local ring B is said to dominate a local ring A if it contains A and the maximal ideal of B contains the maximal ideal...

the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic...

is principal, which shows that any Weil divisor is linearly equivalent to some power of a hyperplane divisor. This consideration proves that the Picard...

F(n)=F\otimes _{{\mathcal {O}}_{X}}{\mathcal {O}}_{X}(n).} 2.  If D is a Cartier divisor and F is an O X {\displaystyle {\mathcal {O}}_{X}} -module (X arbitrary)...

common divisors may be used to find a generator of any ideal. More generally, any two principal ideals in a commutative ring have a greatest common divisor...

polynomial greatest common divisor of two polynomials. Here, "greatest" means "having a maximal degree" or, equivalently, being maximal for the preorder...

computing the primary decomposition, we suppose first that 1 is a greatest common divisor of P and Q. This condition implies that I has no primary component of...

Euclidean Algorithm Generates Traditional Musical Rhythms". The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences...

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...