Solution Found!
Find a subring of Z Z that is not an ideal of Z Z.
Chapter 14, Problem 4E(choose chapter or problem)
QUESTION:
Problem 4E
Find a subring of Z ⊕ Z that is not an ideal of Z ⊕ Z.
Questions & Answers
QUESTION:
Problem 4E
Find a subring of Z ⊕ Z that is not an ideal of Z ⊕ Z.
ANSWER:
Step 1 of 2
Determine a subset of such that it is a subring, but not an ideal.
Consider the subset of .
For any two elements and in ,
So, is closed under subtraction and multiplication. Hence is a subring of .