Talk:Right group

Incorrect definition

One of the axioms in the definition given in the article was incorrect – it stated

"Left identity elements

For all $a\in R$, there is at least one left identity $e$, also in $R$, such that $e\cdot a=a$. Such element does not need to be unique."

However this is not the correct definition of a left identity element because the order of quantifiers is wrong; the above says $\forall a\exists e(ea=a)$, but it should be $\exists e\forall a(ea=a)$ – that is, $e$ should not depend on $a$. I have therefore corrected the article to read

"Left identity elements

There is at least one left identity in $R$. That is, there exists an element $e$ such that $e\cdot a=a$ for all $a$ in $R$. Such an element does not need to be unique."