Answer to Question #350988 in Abstract Algebra for Deq

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 $u ∈ U$, $ru ∈ U$ we have for any $r ∈ R$, $r\cdot1 = r ∈ U$. Hence $R = U$.