The hardest part of the reading for me was visualing some of the examples. For example, thinking of homomorphic rings that aren't isomorphic was a little difficult at first until I realized that the image of the function is a subring of the codomain and that the function is either injective or surjective. Also, I still can't think of any properties that are not preserved by isomorphism.
I think that the concept of isomorphism will make working with rings easier, especially rings constructed from finite sets. Because if the set is finite, there must also be a finite number of distinct, non-isomorphic rings from sets of the same order.
Friday, January 23, 2009
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