# Isomorphism

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• Jun 16th 2013, 12:44 AM
jcir2826
Isomorphism
If A' is isomorphic to A'' and B' is isomorphic to B'' then A'UB' is isomorphic to A''UB''. (their intersections are empty).
Moreover conclude that the disjoint union is well-defined up to isomorphism.
• Jun 16th 2013, 11:39 PM
chiro
Re: Isomorphism
Hey jcir2826.

Can you use results about equivalence classes and partitions for this result? (i.e. show that disjoint equivalence classes have a natural extension to isomorphism results)
• Jun 17th 2013, 09:02 AM
jcir2826
Re: Isomorphism
The would help for the second part.
• Jun 17th 2013, 09:45 AM
emakarov
Re: Isomorphism
Quote:

Originally Posted by jcir2826
If A' is isomorphic to A'' and B' is isomorphic to B'' then A'UB' is isomorphic to A''UB''. (their intersections are empty).

I assume this means A' ∩ B' = ∅ and A'' ∩ B'' = ∅. And what are A', B', A'' and B'': sets, groups, rings, or something else?
• Jun 19th 2013, 10:12 PM
jcir2826
Re: Isomorphism
They are sets. the assumption is correct.