Difficult))) the idea of a coset was a surprise to see with equivalence classes and congruence classes. I remembered it from another math class kindof, so I looked up additional readings to help me understand it better.
That means that R is partitioned into equivalence class under this "congruent to modulo I" relation. The equivalence classes are called "cosets" ... and "the coset of x" just means "the equivalence class of x under the equivalence relation "congruent modulo I"".
Which I got from : http://math.stackexchange.com/questions/23655/what-is-a-quotient-ring-and-cosets
Reflective)))
It's very easy to be reflective with this. I like that the ideal has cosets and that the cosets of a ring are either disjoint or identical. It would be much more helpful if the book actually rewrote the proof and allowed me to compare the differences. It takes a lot more time to read through the old proof and rewrite it to fit the new definitions than it would to just read it...if they had rewritten the proof.
Number theory on cosets and the "circle plus" operator is a handy tool to have under my belt in taking this class...if only it was introduced as clearly then as it was here...should have taken this class first...
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