In abstract algebra, particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is slightly more general than GCDs, and may exist in rings in which GCDs do not. Halter-Koch (1998) provides the following definition. is a maximal common divisor of a subset, , if the following criteria are met: 1. * for all 2. * Suppose , and for all . Then . (Wikipedia).
Greatest Common Divisor (Using Factor Trees to find the Highest Common Factor)
More resources available at www.misterwootube.com
From playlist Computation with Integers
Python: Greatest Common Divisor (GCD)
The greatest common divisor (GCD) is the largest integer that evenly divides two numbers. (GCD is also called the Greatest Common Factor.) For example, the GCD of 21 and 14 is 7. This video shows you a beautiful recursive definition of GCD and how to write it in Python.
From playlist Python
From playlist Abstract Algebra 2
Discrete Math - 4.3.2 Greatest Common Divisors and Least Common Multiples
Finding the greatest common divisor and least common multiple using the method of primes. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Discrete Math - 4.3.4 Greatest Common Divisors as Linear Combinations
Writing the greatest common divisor of two integers as a linear combination of those integers. Bezout's Theorem is also covered. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Two strategies for finding the greatest common factor or greatest common divisor or highest common factor/divisor. These all refer to the same number.
From playlist Arithmetic and Pre-Algebra: Factors and Multiples
Maria Angelica Cueto - "Implicitization of surfaces via geometric tropicalization"
Implicitization of surfaces via geometric tropicalization - Research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
C. Soulé - Arithmetic Intersection (Part2)
Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic intersection number of ¯L and ¯M. We shall explain the definition and the basic properties of
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
From playlist Abstract Algebra 2
Introduction to Number Theory, Part 2: Greatest Common Divisors
The second video in a series about elementary number theory. We define the greatest common divisor of two numbers, and prove a useful theorem.
From playlist Introduction to Number Theory
CTNT 2020 - The global field Euler function. Santiago Arango-Piñeros.
The paper is available at https://arxiv.org/abs/2005.04521?fbclid=IwAR34njBRG6gEAjzQqdk7johkPEC5i4c5Bbq1MJtyeNAZ95yeQWvaiys2LF0 Comments very welcome!
From playlist CTNT 2020 - Conference Videos
Highest Common Factor & Lowest Common Multiple - GCSE Mathematics
How to find the highest common factor and lowest common multiple (hcf and lcm) of any two numbers using prime factors. ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️ https://www.youtube.com/channel/UCf89Gd0FuNUdWv8FlSS7lqQ/join
From playlist Number
C. Soulé - Arithmetic Intersection (Part3)
Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic intersection number of ¯L and ¯M. We shall explain the definition and the basic properties of
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
RNT2.1. Maximal Ideals and Fields
Ring Theory: We now consider special types of rings. In this part, we define maximal ideals and explore their relation to fields. In addition, we note three ways to construct fields.
From playlist Abstract Algebra
Chinese Remainder Theorem and Geometry of Unipotents - Feb 12, 2021- Rings and Modules
In this video we prove a version of the chinese remainder theorem and explain how unipotent elements are related to connected components of schemes.
From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]
This video explains how to determine the GCF of integers and expressions. http://mathispower4u.wordpress.com/
From playlist Integers
Commutative algebra 49: Completions
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define the completion of a ring and give some examples: the ring of formal power series, and the ring of 10-adic integers.
From playlist Commutative algebra
RNT2.2. Principal Ideal Domains
Ring Theory: We define PIDs and UFDs and describe their relationship. Prime and irreducible elements are defined, and conditions for implication are given. (second version: corrections to definition of prime and irreducible; comment should be 'R UFD implies R[x] UFD, improved proof that
From playlist Abstract Algebra
Using the TI84 to Help Factor Out the GCF of an Expression
This video explains how to use the TI84 to determine the GCF of 2 or 3 integers.
From playlist Determining the Greatest Common Factor and Factoring by Grouping