Exercise
What about the union of a collection C of subrings of R?
The union is also a subring.
The union need not be a subring, but it does occur.
The union is never a subring.
No. Think of the subrings
Q+Q
2 and
Q+Q3.
The product 6 of
2 and
3 does not
belong to the union.
2 and
Q+Q3.
The product 6 of
2 and
3 does not
belong to the union.
Indeed.
No.
For example, if the collection C consists of a single
subring, the union is a subring.