Jump to content

Talk:Annihilator (ring theory)

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

Untitled

[edit]

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

Confusing tag?

[edit]

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

Article improvements

[edit]
  • 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

[edit]

Noncommutative examples

[edit]

Additional references

[edit]

this article is full of lies

[edit]

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]