http://mysite.science.uottawa.ca/kzaynull/MAT4145/mat4145.htmlI need to do those ex in link above and the passwordis ring2.9, 4.11,10.10,10.14,

Solution: 2
Solution: 2.1: the ring to be isomorphic should follow the following properties:
1. Define a function f : R → S, which you think will be an isomorphism.
2. Prove that f is a one-to-one function.
3. Prove that f is onto.
4. Prove that f (xy) = f(x) f(y) for all x, y ∈ R.
Assume that
1
:()(,)
fRtRtt
-
®

This function is a bijective function from
1
:()(,)
fRtRtt
-
®
or
1
ttot
-
which
becomes impossible because R (t) is countable.
The function
1
:()(,)
fRtRtt
-
®
 , is bijective, since for...