In ring theory, a branch of mathematics, a ring is called a reduced ring if it has no non-zero nilpotent elements. Equivalently, a ring is reduced if it has no non-zero elements with square zero, that is, x2 = 0 implies x = 0. A commutative algebra over a commutative ring is called a reduced algebra if its underlying ring is reduced. The nilpotent elements of a commutative ring R form an ideal of R, called the nilradical of R; therefore a commutative ring is reduced if and only if its nilradical is zero. Moreover, a commutative ring is reduced if and only if the only element contained in all prime ideals is zero. A quotient ring R/I is reduced if and only if I is a radical ideal. Let D be the set of all zero-divisors in a reduced ring R. Then D is the union of all minimal prime ideals. Over a Noetherian ring R, we say a finitely generated module M has locally constant rank if is a locally constant (or equivalently continuous) function on Spec R. Then R is reduced if and only if every finitely generated module of locally constant rank is projective. (Wikipedia).
Math Basics: Reducing Fractions
In this video, you’ll learn more about reducing fractions. Visit https://www.gcflearnfree.org/fractions/comparing-and-reducing-fractions/1/ for our interactive text-based lesson. This video includes information on: • Comparing fractions with different denominators • Reducing fractions • U
From playlist Math Basics
Learn how to determine the product of two fractions with unlike denominators
👉 Learn how to multiply fractions. To multiply fractions, we need to multiply the numerator by the numerator and multiply the denominator by the denominator. We then reduce the fraction. By reducing the fraction we are writing it in most simplest form. It is very important to understand t
From playlist How to Multiply Fractions
👉 Learn how to multiply fractions. To multiply fractions, we need to multiply the numerator by the numerator and multiply the denominator by the denominator. We then reduce the fraction. By reducing the fraction we are writing it in most simplest form. It is very important to understand t
From playlist How to Multiply Fractions
👉 Learn how to multiply fractions. To multiply fractions, we need to multiply the numerator by the numerator and multiply the denominator by the denominator. We then reduce the fraction. By reducing the fraction we are writing it in most simplest form. It is very important to understand t
From playlist How to Multiply Fractions
Fraction misconception adding the numerator and the denominator
👉 Learn how to add or subtract fractions with common denominators. When adding or subtracting two or more fractions with common denominators, we add or subtract only the numerator while we keep the denominator the same. We will then simplify our answer by reducing the fraction if necessar
From playlist Add and Subtract Fractions with Like Denominators
Algebra - Reducing a fraction to lowest terms
This video describes how to reduce a fraction to lowest terms. For more videos visit mysecretmathtutor.com
From playlist Algebra
Adding fractions with like denominators - math homework answers
👉 Learn how to add or subtract fractions with common denominators. When adding or subtracting two or more fractions with common denominators, we add or subtract only the numerator while we keep the denominator the same. We will then simplify our answer by reducing the fraction if necessar
From playlist Add and Subtract Fractions with Like Denominators
How to subtract fractions with like denominators and proper answers
👉 Learn how to add or subtract fractions with common denominators. When adding or subtracting two or more fractions with common denominators, we add or subtract only the numerator while we keep the denominator the same. We will then simplify our answer by reducing the fraction if necessar
From playlist Add and Subtract Fractions with Like Denominators
Learn How To Reduce A Fraction – Be A Math Superstar :)
TabletClass Math: https://tcmathacademy.com/ This video explains how to reduce a fraction by cancelling like factors found in the numerator and denominator – reducing fractions is a key skill in math and in algebra.
From playlist Pre-Algebra
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
Log Volume Computations - part 0.2 - Total Rings Of Fractions
This is the second part of the prerequisite videos for the log volume computations and is optional for continuing. In this video we explain how to take rings of fractions for reduced but not irreducible rings. We then show that the ring of fractions of a tensor product is the tensor prod
From playlist Log Volume Computations
Georg Regensburger, University of Kassel
March 22, Georg Regensburger, University of Kassel Integro-differential operators with matrix coefficients
From playlist Spring 2022 Online Kolchin seminar in Differential 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
Purity for flat cohomology by Kestutis Cesnavicius
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
The Simplifying Synthesis Ultimate Guide To Rules for Ring Closure
An organic chemistry lesson on Baldwins Rules and Beckwith Rules for ring closing reactions. SUPPORT THE CHANNEL ON PATREON: https://www.patreon.com/SimplifyingSy... Socials: https://www.instagram.com/simplifying... https://twitter.com/SimplifyingSyn1 https://www.facebook.com/Simplifyi
From playlist Ultimate Guides
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We use the fiber product define last lecture to define group schemes, and give a few non-classical examples of them.
From playlist Algebraic geometry II: Schemes
Automorphy: Automorphy Lifting Theorems I (continued)
David Geraghty Princeton University; Institute for Advanced Study March 10, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Reducing a Fraction to Lowest Terms
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Reducing a Fraction to Lowest Terms. Here I look at reducing a fraction to lowest terms. I do not take the shortest route, but show how I often perform the s
From playlist All Videos - Part 2
Lexicon of Biochemical Reactions: Redox Cofactors
MIT 5.07SC Biological Chemistry, Fall 2013 View the complete course: http://ocw.mit.edu/5-07SCF13 Instructor: JoAnne Stubbe In this video, Professor Stubbe reviews oxidation and reduction and the cofactors that are involved in these transformations. She focuses on the two redox active cof
From playlist MIT 5.07SC Biological Chemistry I, Fall 2013