Ring theory

Torsion-free module

In algebra, a torsion-free module is a module over a ring such that zero is the only element annihilated by a regular element (non zero-divisor) of the ring. In other words, a module is torsion free if its torsion submodule is reduced to its zero element. In integral domains the regular elements of the ring are its nonzero elements, so in this case a torsion-free module is one such that zero is the only element annihilated by some non-zero element of the ring. Some authors work only over integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the ring contains zero-divisors then the only module satisfying this condition is the zero module. (Wikipedia).

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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 finish the survey of types of modules by briefly discussing torsion-free and coprimary modules. We show that flat modules a

From playlist Commutative algebra

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Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the equation of torque=? of the torsion of a hollow tube. Next video in this series can be found at: https://youtu.be/mQ-wseAfAlc

From playlist PHYSICS 16.6 TORSION

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Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with many rings,and transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2014,AkiraNishihara

From playlist 3D printed toys

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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is torsion and the variables associated with twisting of a steel rod. Next video in this series can be found at: https://youtu.be/jlt6Jy59nJs

From playlist PHYSICS 16.6 TORSION

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Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

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From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]

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Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf

From playlist Abstract Algebra 2

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From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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From playlist Commutative algebra

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From playlist Mathematics

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From playlist An Introduction to the Arithmetic of Elliptic Curves

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Visit http://ilectureonline.com for more math and science lectures! In this video I will find f=? and T=? of a cable suspending a rod with 2 masses one on each end of the rod. Next video in this series can be found at: https://youtu.be/WGHEXoCGXVY

From playlist PHYSICS 16.6 TORSION

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From playlist Commutative algebra

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From playlist Global Noncommutative Geometry Seminar (Europe)

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From playlist 3D printed toys

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Related pages

Integral domain | Flat cover | Torsion (algebra) | Ideal (ring theory) | Associated prime | Automorphism | Isomorphism | Torsionless module | Absorbing element | Principal ideal domain | Torsion-free abelian group | Polynomial ring | Quotient module | Free module | Dedekind domain | Field (mathematics) | Noetherian ring | Sheaf (mathematics) | Ring (mathematics) | Integrally closed domain | Scheme (mathematics) | Abstract algebra | Restriction (mathematics) | Endomorphism | Module (mathematics)