Commutative algebra | Algebraic structures | Ring theory
In algebra, the integral closure of an ideal I of a commutative ring R, denoted by , is the set of all elements r in R that are integral over I: there exist such that It is similar to the integral closure of a subring. For example, if R is a domain, an element r in R belongs to if and only if there is a finitely generated R-module M, annihilated only by zero, such that . It follows that is an ideal of R (in fact, the integral closure of an ideal is always an ideal; see below.) I is said to be integrally closed if . The integral closure of an ideal appears in a theorem of Rees that characterizes an analytically unramified ring. (Wikipedia).
Commutative Algebra - Integral Closures - part 03 - Integral Closedness is Local (an Normality)
In this video we show that being integrally closed is a local property.
From playlist Integral Closures
Commutative Algebra - Integral Closures - part 01 - Basics
This is a video for a second semester graduate algebra class.
From playlist Integral Closures
Find the value of the integral with e
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Use the area of triangles to represent the integral
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Find the area enclosed by the two curves
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
How to use u substitution to find the indifinite integral
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
What is an integral and it's parts
👉 Learn about integration. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which the upper and the lower li
From playlist The Integral
Schemes 14: Irreducible, reduced, integral, connected
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We discuss the 4 properties of schemes: reduced, irreducible, integral, and connected.
From playlist Algebraic geometry II: Schemes
Learn how to evaluate the integral of a constant
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Commutative Algebra - Integral Closure - part 02 - Going Up
Going up Theorem. https://en.wikipedia.org/wiki/Going_up_and_going_down
From playlist Integral Closures
Find the area enclosed by the two curves using two integrals
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Introduction to the category of Adic spaces (Lecture 2) by Utsav Choudhury
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Commutative algebra 34 Geometry of normalizations
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 discuss the geometric meaning of finite morphisms and normal rings. Finite morphisms have the property that in the map of
From playlist Commutative algebra
Log Volume Computations - part 0.3 (optional) - Integral Closures
This video isn't strictly necessary for what was going on but answers some questions about rings of integers and integral closures for non-reduced rings. In this video we show that what we have been calling OO_L for L a tensor product of fields is actually the integral closure of OO_{K_1}
From playlist Log Volume Computations
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Maryna Viazovska - 4/6 Automorphic Forms and Optimization in Euclidean Space
Hadamard Lectures 2019 The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and I
From playlist Hadamard Lectures 2019 - Maryna Viazovska - Automorphic Forms and Optimization in Euclidean Space
Apply u substitution to a polynomial
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral