Definition talk:Principal Ideal of Ring

As multiplication is not necessarily associative, this will only be a left ideal. The proof of Principal Ideal is an Ideal skims over this. I suppose it is an omission in the definition. --Lord_Farin 14:38, 23 October 2011 (CDT)
 * Yes, you're right - I've seen a distinction being made between left & right ideals in various sites on the web, but not in any of the books I've actually come into contact with. Feel free to attack this area with your usual gusto. --prime mover 14:41, 23 October 2011 (CDT)

My approach is radically different:

Proposed definition: A principal ideal is an ideal that is generated by a single element $a$.

This is (AFAIK) the usual definition of a principal ideal. --Lord_Farin 15:15, 23 October 2011 (CDT)