Abstract Algebra | Properties and examples of ring homomorphisms.

[@ashishKjr]

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

[@MichaelPennMath]

Yes, these are already in my overall plan.

[@darrenpeck156]

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

[@JaredCai]

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

[@maxdickens9280]

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.

[@darrenpeck156]

How do we know n has an inverse for division?

[@darrenpeck156]

Great examples!!!

[@darrenpeck156]

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?

[@asht750]

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

[@maxdickens9280]

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.

[@abnerandreymartinezzamudio3366]

He did explain that n ≠ 0 because φ is injective so 0 can only map to 0

[@carlosdominguez9420]

Thanks Bro