Answer to Question #351024 in Abstract Algebra for Fed

Question

3.5 If U is an ideal of R and 1 ∈ U, prove that U = R.

Answer 1

Since for any $r\in R$ and $u\in U$, $ru\in U$ we have for any $r\in R$, $r\cdot 1=r\in U$. Hence $R=U$.