Abstract Algebra | More ring theory examples.

We present some more examples involving rings. Among other things, we prove results about ideals and homomorphisms in matrix and polynomial rings.

[nailabenali]

I really like the world of abstract algebra.. I was wondering if you were intersting in analysis too? I mean in the proofs more than the technical aspect.. For example all the great stuffs of power series and not only finding the radius of convergence using the ratio test ( I don't really understand why every video I've watched uses this method like it's the only one ) anyway I hope u'll do a playlist for analysis too! Thank you again

[unhealthytruthseeker]

There's actually an easier way to show the even linear term is not an ideal. Just choose f(x) = x. Then the resultant polynomial will have lx as its linear term. If l is odd, it's not part of the "ideal." Since there are no restrictions on l, it can be odd, so you don't have an ideal.