Abstract Algebra | Properties and examples of ring homomorphisms.

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We present some important properties of ring homomorphisms and give some examples. For instance we prove that 2Z and 3Z are isomorphic as groups but not rings.

  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
Автор

At 12:44:
Michael didn't solve the equation correctly. In fact, n=0 is an additional solution for 6n = 9n^2.
Nonetheless, this implies that the homomorphism simply maps every number to zero, resulting in a trivial homomorphism.

maxdickens
Автор

Hello! Can you make some videos on Orbit Stabilizer theorem, Class equation, Sylow's theorem?

ashishKjr
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12:44 I think he meant there's no ring isomorphism(where he said homomorphism) from 2Z to 3Z.

JaredCai
Автор

Don't we need to be in Q for n to have an inverse, but we are only in Z. It seems to be a big problem. Unless we are in Z mod 3?

darrenpeck
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Some textbooks use the additive group or subgroup as a condition to prove if a subset of a ring is ideal.

asht
Автор

How do we know n has an inverse for division?

darrenpeck