Answer to Question #16543 in Algebra for Tsit Lam

Question #16543
Let R be a ring possibly without an identity. Show that if R has a unique left identity e, then e is also a right identity
1
Expert's answer
2012-10-17T09:21:39-0400
Suppose e ∈ R is a unique left identity for R. Then for any a, c ∈ R,
(e + ae − a)c = c + ac − ac = c.
Therefore, e + ae − a = e, which implies ae = a (for any a ∈ R).

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS