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)


 * All I've got is what my books tell me and they clearly give an incomplete definition. Your radically different approach is not so different from the definition given, if you click on "generated" and it goes to "Generator of an Ideal" etc. Except that the definition of ideal that you have is the union of the left and right ideal, it (shrug) looks the same to me. What's your source work? --prime mover 15:45, 24 October 2011 (CDT)