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Wednesday, November 4, 2009

Watched lecture 6 of Abstract Algebra E-222

( A lecture by Peter again ).
Arithmetic congruent mod n.
How a congruent b mod n is in fact an equivalence relation.
And thus induces a partition of the integers.
Cosets are nZ, 1+nZ, 2+nZ, ... (n-1)+nZ
Addition can be defined on these cosets and then they have a group structure.
The map Z -> nZ is then a homomorphism with 0 as kernel.

( Around min 35 or so I lost interest... I fast forwarded watching minutes here and there, just to make sure there was not introduced anything I did not know already. I hope I am not losing interest in the series all together. We'll see. )

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