Solution Found!
Let R be the ring of continuous functions from R to R. Let
Chapter 14, Problem 55E(choose chapter or problem)
QUESTION:
Let R be the ring of continuous functions from \(\mathbf{R}\) to \(\mathbf{R}\). Let \(A= \{f \in R \mid f(0)\) is an even integer \(\}\). Show that A is a subring of R, but not an ideal of R.
Questions & Answers
QUESTION:
Let R be the ring of continuous functions from \(\mathbf{R}\) to \(\mathbf{R}\). Let \(A= \{f \in R \mid f(0)\) is an even integer \(\}\). Show that A is a subring of R, but not an ideal of R.
ANSWER:Step 1 of 3
We first prove that 
