In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers. The ring of integers of a number field K, denoted by OK, is the intersection of K and A: it can also be characterised as the maximal order of the field K. Each algebraic integer belongs to the ring of integers of some number field. A number α is an algebraic integer if and only if the ring is finitely generated as an abelian group, which is to say, as a -module. (Wikipedia).
Ex: Write a Algebraic Expression in the Form x+c and c-x (less and more)
This video explains how to write a algebraic or variable expression from a given statement. http://mathispower4u.com
From playlist Evaluating and Writing Algebraic Expressions
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
What is the Difference Between Rational and Irrational Numbers , Intermediate Algebra , Lesson 12
This tutorial explains the difference between rational and irrational numbers. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)
From playlist Intermediate Algebra
Field Theory: We consider the property of algebraic in terms of finite degree, and we define algebraic numbers as those complex numbers that are algebraic over the rationals. Then we give an overview of algebraic numbers with examples.
From playlist Abstract Algebra
The integers modulo n under addition is a group. What are the integers mod n, though? In this video I take you step-by-step through the development of the integers mod 4 as an example. It is really easy to do and to understand.
From playlist Abstract algebra
Evaluating Algebraic Expressions
In this video we discuss the basic principles for evaluating algebraic expressions, including order of operations and the importance of parentheses.
From playlist College Algebra
Determining if a equation is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Learn how to identify if a function is a polynomial and identify the degree and LC
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
[ANT13] Dedekind domains, integral closure, discriminants... and some other loose ends
In this video, we see an example of how badly this theory can fail in a non-Dedekind domain, and so - regrettably - we finally break our vow of not learning what a Dedekind domain is.
From playlist [ANT] An unorthodox introduction to algebraic number theory
The sum of 4 consecutive integers is 334. Find the integers.
How to solve an algebra word problem about consecutive integers. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review n
From playlist GED Prep Videos
The sum of three consecutive integers plus 5 is 20. What are the numbers?
How to solve an algebra word problem involving consecutive integers. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, revi
From playlist GED Prep Videos
The sum of three consecutive integers is 18, what are the numbers?
How to solve an algebra word problem about consecutive integers. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review
From playlist GED Prep Videos
This lecture is part of an online graduate course on Galois theory. We define the norm and trace of a finite extension of fields. We give some examples of calculating the image of the norm map, and show how to use the norm and trace to find rings of algebraic integers.
From playlist Galois theory
The ratio of an integer and 2 less than that integer is 2/3. Find the integer.
How to solve an algebra word problem about ratios. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizz
From playlist GED Prep Videos
Visual Group Theory: Lecture 7.5: Euclidean domains and algebraic integers
Visual Group Theory: Lecture 7.5: Euclidean domains and algebraic integers. Around 300 BC, the Greek mathematician Euclid found an algorithm to compute the greatest common divisor (gcd) of two numbers. Loosely speaking, a Euclidean domain is a commutative ring for which this algorihm stil
From playlist Visual Group Theory
Samit Dasgupta: An introduction to auxiliary polynomials in transcendence theory, Lecture I
Broadly speaking, transcendence theory is the study of the rationality or algebraicity properties of quantities of arithmetic or analytic interest. For example, Hilbert’s 7th problem asked ”Is a b always transcendental if a 6= 0, 1 is algebraic and b is irrational algebraic?” An affirmativ
From playlist Harmonic Analysis and Analytic Number Theory
Digression: THH of the integers (corrected)
In this video, we explain how to compute THH of the integers. In order to do this we compute it first relative to the element p and then use a spectral sequence to deduce the final result. This is a corrected version of the old video, in which I got the Hasse-squares at 13:10 and 24:20 w
From playlist Topological Cyclic Homology
Algebra NUMBER WORD PROBLEM – Let’s solve it step-by-step…
TabletClass Math: https://tcmathacademy.com/ Algebra number word problem involving consecutive integers. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Note
From playlist GED Prep Videos