Talk:Annihilator (ring theory)

Latest comment: 3 years ago by 70.171.155.43 in topic this article is full of lies

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Annihilators in ring theory and linear algebra need separate treatments I think. Geometry guy 00:39, 22 May 2007 (UTC)Reply

Confusing tag?

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Please indicate which sections are the most confusing, thanks :) Rschwieb (talk) 01:41, 25 June 2011 (UTC)Reply

Article improvements

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  • Expand the definitions section to include the definition of annihilator for commutative rings
  • Also create subsections for left and right annihilators for noncommutative rings
  • Partition references by commutative and non-commutative references
  • Include references to noncommutative rings

Noncommutative properties

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Noncommutative examples

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Additional references

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this article is full of lies

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what the heck happened here?!?! 70.171.155.43 (talk) 20:36, 30 January 2021 (UTC)Reply

Here is the first lie excised from the article:

The prototypical example for an annihilator over a commutative ring can be understood by taking the quotient ring   and considering it as a  -module. Then, the annihilator of   is the ideal   since all of the   act via the zero map on  . This shows how the ideal   can be thought of as the set of torsion elements in the base ring   for the module  . Also, notice that any element   that isn't in   will have a non-zero action on the module  , implying the set   can be thought of as the set of orthogonal elements to the ideal  . — Preceding unsigned comment added by 70.171.155.43 (talk) 20:41, 30 January 2021 (UTC)Reply

This is the second one, a false proof of the first:

In particular, if   then the annihilator of   can be found explicitly using

 

Hence the annihilator of   is just  . 70.171.155.43 (talk) 20:46, 30 January 2021 (UTC)Reply