Abstract Algebra | Properties and examples of ring homomorphisms.

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...

[@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?

[@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!!!

[@darrenpeck156]

How do we know n has an inverse for division?

[@asht750]

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

[@carlosdominguez9420]

Thanks Bro

[@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.

[@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.