What is Torsion: Definition and 236 Discussions

In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements. A torsion module is a module that equals its torsion submodule. A module is torsion free if its torsion submodule is reduced to the zero element.
This terminology is more commonly used for modules over a domain, that is, when the regular elements of the ring are all its nonzero elements.
This terminology applies to abelian groups (with "module" and "submodule" replaced by "group" and "subgroup"). This is allowed by the fact that the abelian groups are the modules over the ring of integers (in fact, this is the origin of the terminology, that has been introduced for abelian groups before being generalized to modules).
In the case of groups that are noncommutative, a torsion element is an element of finite order. Contrarily to the commutative case, the torsion elements do not form a subgroup, in general.

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  1. EnigmaticField

    A Nonvanishing Torsion: When Does It Occur?

    Since the first day I learned the torsion I keep having the question how a nonvanishing torsion is likely to occur because based on the definition formula of the torsion, it looks like the torsion always vanishes. I have come back to think about this question a couple of times after my first...
  2. P

    A Connection, Metric and Torsion

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  3. F

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  4. N

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  5. M

    I Torsion on cylinder described differentially

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  6. P

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  7. R

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  8. B

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  9. Urs Schreiber

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  10. T

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  12. thegreengineer

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  13. P

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  14. mertcan

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  15. Alistair McCheyne

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  16. J

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  17. C

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  18. S

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  19. itssilva

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  22. F

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  23. Feodalherren

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  24. N

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  25. P

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  26. O

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  27. R

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  28. Q

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  29. Y

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  30. binbagsss

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  31. G

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  32. M

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  33. jonny23

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  34. W

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  35. B

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  36. R

    Building a fold down door with torsion gas spring calculation

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  37. G

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  38. kroni

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  39. D

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  40. A

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  41. N

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  42. C

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  43. M

    Understanding Torsion of Curve: Normal Unit Vector Explanation

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  44. T

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  45. Demon117

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  46. J

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  47. V

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  48. H

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  49. A

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  50. D

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