In algebra and algebraic geometry, given a commutative Noetherian ring and an ideal in it, the n-th symbolic power of is the ideal where is the localization of at , we set is the canonical map from a ring to its localization, and the intersection runs through all of the associated primes of . Though this definition does not require to be prime, this assumption is often worked with because in the case of a prime ideal, the symbolic power can be equivalently defined as the -primary component of . Very roughly, it consists of functions with zeros of order n along the variety defined by . We have: and if is a maximal ideal, then . Symbolic powers induce the following chain of ideals: (Wikipedia).
"Understand power notation and calculate simple powers, e.g. squares, cubes."
From playlist Number: Powers, Roots & Laws of Indices
You MUST Harness the ‘Power of Intention’ When Learning Anything
The power of intention refers to the ability of a person to direct their thoughts and energy towards a specific goal or outcome. This concept is often associated with positive thinking and the law of attraction, which suggests that individuals can manifest their desires through the power o
From playlist Life Hacks
Philosophy means, in Ancient Greek, the love of wisdom. But the word wisdom can sound very big and forbidding; what does it really mean to be wise? And how might we consciously strive to be a little wiser? If you like our films take a look at our shop (we ship worldwide): http://www.thesch
From playlist SELF
Imaginary Numbers, Functions of Complex Variables: 3D animations.
Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.
From playlist Physics
Learn how to use power to quotient rule to simplify an expression with rational power
Learn how to evaluate numbers raised to rational powers. When given a number raised to a rational power, we take the nth root of the number where n is the number in the denominator of the rational power, then we raise the result to a power equivalent to the number in the numerator of the r
From playlist Numbers Raised to Fractional Exponents
Learn how to rewrite an exponent with a fraction power as an radical expression
Learn how to evaluate numbers raised to rational powers. When given a number raised to a rational power, we take the nth root of the number where n is the number in the denominator of the rational power, then we raise the result to a power equivalent to the number in the numerator of the r
From playlist Numbers Raised to Fractional Exponents
How to simplify a exponent with a negative rational power
Learn how to evaluate numbers raised to rational powers. When given a number raised to a rational power, we take the nth root of the number where n is the number in the denominator of the rational power, then we raise the result to a power equivalent to the number in the numerator of the r
From playlist Numbers Raised to Fractional Exponents
Commutative algebra 30 Symbolic powers
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. In this lecture we give some examples related to primary ideals. In particular we give an example of a primary ideal that is
From playlist Commutative algebra
[ANT12] Quadratic reciprocity and prime factorisation
In this video, we finally put all the pieces together and see how quadratic reciprocity can help us to factorise primes in quadratic extensions of Z. ANT books: Marcus, "Number Fields"; Ireland and Rosen, "A Classical Introduction to Modern Number Theory"... Keith Conrad's notes: https:/
From playlist [ANT] An unorthodox introduction to algebraic number theory
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
An Application of a Conjecture of Mazur-Tate to Supersingular Elliptic Curves - Emmanuel Lecouturier
Joint IAS/Princeton University Number Theory Seminar Topic: An Application of a Conjecture of Mazur-Tate to Supersingular Elliptic Curves Speaker: Emmanuel Lecouturier Affiliation: Tsinghua University Date: February 14, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Set Theory (Part 18): The Rational Numbers are Countably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will show that the rational numbers are equinumerous to the the natural numbers and integers. First, we will go over the standard argument listing out the rational numbers in a table a
From playlist Set Theory by Mathoma
Modular symbols and arithmetic - Romyar Sharifi
Locally Symmetric Spaces Seminar Topic: Modular symbols and arithmetic Speaker: Romyar Sharifi Affiliation: University of California; Member, School of Mathematics Date: January 16, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction To Beilinson--Kato Elements And Their Applications 2 by Chan-Ho Kim
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
How to apply the power to power rule with rational exponents
👉 Learn how to simplify rational powers using the power rule. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the power rule which states that when an expression with an exponent is raised to another exponent tha
From playlist Raise an Exponent to a Fraction
Social Equality & the Problem of Hierarchy (Jonathan Wolff)
Professor Jonathan Wolff (University of Oxford) gives a talk on Equality and Hierarchy in 2018 as part of The Aristotelian Society. For more information: www.aristoteliansociety.org.uk More Political Philosophy: https://www.youtube.com/playlist?list=PLhP9EhPApKE_O1dkCOqsUke_0QUkX80A- #Ph
From playlist Social & Political Philosophy
Electric Potential Difference and Circuit Basics
The following topics are discussed: Electric Potential Energy, Electric Potential Difference, Electromotive Force, emf, Terminal Voltage, Basic Circuits, Current Direction, open, closed, and short circuits, electrical load, and light bulb symbols in circuits. Electric potential difference
From playlist All of AP Physics C: Electricity & Magnetism!
Ideal sources | Circuit analysis | Electrical engineering | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/circuit-elements/v/ee-ideal-sources Introduction to the voltage source and current source. Created by Willy Mc
From playlist Circuit analysis | Electrical Engineering | Khan Academy
Do you know the definition for power? It's a commonly used word but you'll have to be more specific when using it in Physics. Still looking for a tutor for National 5 Physics? Take a look at my website for details and to find out if I still have availability. #shorts
From playlist Shorts
CTNT 2020 - Computations in Number Theory (by Alvaro Lozano-Robledo) - Lecture 3
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Computations in Number Theory Research