Abstract Algebra | Properties and examples of ring homomorphisms.

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Күн бұрын

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.
www.michael-penn.net
www.researchgate.net/profile/...
www.randolphcollege.edu/mathem...

Пікірлер: 11

@darrenpeck156 Жыл бұрын

Great examples!!!

@asht750 3 жыл бұрын

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

@darrenpeck156 Жыл бұрын

How do we know n has an inverse for division?

@darrenpeck156 Жыл бұрын

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?

@ashishKjr 4 жыл бұрын

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

@MichaelPennMath 4 жыл бұрын

Yes, these are already in my overall plan.

@darrenpeck156 Жыл бұрын

Please make these videos. I love the involved long examples; it's like story telling!!!

@JaredCai Жыл бұрын

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

@maxdickens9280 9 ай бұрын

He 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.

@maxdickens9280 9 ай бұрын

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.