Ring theory | Module theory

Singular submodule

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).

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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)

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From playlist Real Analysis

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From playlist Adding and Subtracting Fractions

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From playlist Addition and Subtraction of Whole Numbers

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From playlist Differential Equations

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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)

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From playlist Global Noncommutative Geometry Seminar (Americas)

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From playlist Abstract Algebra 2

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From playlist How to Solve Multi Step Equations with Variables on Both Sides

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From playlist Course 1: Precalculus (Fall 2022)

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