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."