In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R-module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as . For general rings, is a good generalization of the torsion submodule tors(M) which is most often defined for domains. In the case that R is a commutative domain, . If R is any ring, is defined considering R as a right module, and in this case is a two-sided ideal of R called the right singular ideal of R. The left handed analogue is defined similarly. It is possible for . (Wikipedia).
An introduction to subtraction, the terms and concepts involved, and subtraction as the opposite of addition. Some example problems are carefully worked and explained. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 1 (Complete chapter)
Intro to Subsequences | Real Analysis
What are subsequences in real analysis? In today's lesson we'll define subsequences, and see examples and nonexamples of subsequences. We can learn a lot about a sequence by studying its subsequence, so let's talk about it! If (a_n) is a sequence, we can denote a subsequence of (a_n) as (
From playlist Real Analysis
Ex 2: Subtracting Signed Fractions
This video provides two examples of subtracting signed fractions. Complete Video Library at http://www.mathispower4u.com
From playlist Adding and Subtracting Fractions
Determine a Subtraction Problem Modeled on a Number Line
This video explains how to write an subtraction equation from a number line model. http://mathispower4u.com
From playlist Addition and Subtraction of Whole Numbers
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Yi Wang: The Helton-Howe trace formula on submodules
Talk by Yi Wang in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on August 19, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Solving a multi-step equation by multiplying by the denominator
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Josef Teichmann: An elementary proof of the reconstruction theorem
CIRM VIRTUAL EVENT Recorded during the meeting "Pathwise Stochastic Analysis and Applications" the March 09, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Virtual Conference
From playlist Abstract Algebra 2
Submodule GB01 Game Boy Cart Reader: Lots of Potential!
Cartridge readers are a common staple among Game Boy enthusiasts. Does a new contender from Submodule have what it takes to stand out? Submodule GB01: https://submodule.co/ ----------------------------------------Â------------------------------------- Please consider supporting my work
From playlist Tech Reviews
Lecture 17. Isomorphism theorems. Free modules
0:00 0:19 1st isomorphism theorem 1:15 2nd isomorphism theorem 4:56 3rd isomorphism theorem 9:40 Submodules of a quotient module 12:55 Generators 18:34 Finitely generated modules 30:21 Cautionary example: not every submodule of a finitely generated module is finitely generated 33:18 Linea
From playlist Abstract Algebra 2
Francesco Vaccarino (8/4/21): Parallel decomposition of persistence modules through interval bases
We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an "interval basis". This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the
From playlist AATRN 2021
Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
Solving a multi-step equation with fractions and variable on both sides
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Solving a one step equation with subtraction
👉 Learn how to solve a one step equation. An equation is a statement stating that two values are equal. A one step equation is an equation whose solution can be obtained by performing only one step of operation on the equation. To solve a one step addition/subtraction equation, we isolate
From playlist How to Solve One Step Equations with Addition
Lecture 19. Structure of modules
From playlist Abstract Algebra 2
Math 023 Fall 2022 120722 Introduction to Complex Numbers (Arithmetic)
Problem with real numbers: no solution to x^2 = -1. So we adjoin a symbol, i, to the real numbers, and require that all the basic laws (commutativity, associativity, distributivity, etc.) hold. Definition of complex number: a+bi, where a, b are real numbers. Definition of real part, com
From playlist Course 1: Precalculus (Fall 2022)
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra