Definition talk:Division Ring

Alternative Definitions are a bit unclear to me. It seems that $\left(1\right)$ and $\left(2\right)$ are independent, equivalent definitions, whereas $\left(3\right)$ merely follows from the definition. Please correct me, if I am wrong, though.

Also, perhaps drop uniqueness from the definition, since it follows by Product Inverses in Ring are Unique. -- TheSpleen (talk) 16:06, 8 September 2013 (UTC)