Recent content by RVP91

A-modules.

Homework Statement Let A be a commutative ring with identity element. Prove that HomA(M,HomA(N,K)) is isomorphic to HomA(N,HomA(M,K)). Homework Equations The Attempt at a Solution I believe it is best to start by defining a map, f: HomA(M,HomA(N,K) → HomA(N,HomA(M,K)) for ψ: M...

If I was to try to work this out I would use the Chinese Remainder Theorem and since 10557 = 3^3 . 17 . 23 end up with (Z/10557Z)* isomorphic to (Z/27Z)* x (Z/17Z)* x (Z/23Z)* isomorphic to C18 x C16 x C22 where Cn represents the Cyclic group order n. How would I then write this as Cn1 x Cn2...

If I was to try to work this out I would use the Chinese Remainder Theorem and since 10557 = 3^3 . 17 . 23 end up with (Z/10557Z)* isomorphic to (Z/27Z)* x (Z/17Z)* x (Z/23Z)* isomorphic to C18 x C16 x C22 where Cn represents the Cyclic group order n. How would I then write this as Cn1 x Cn2...

Oh right. I'm really confused now. Is there any chance you could perhaps give me the first few lines of the proof and then some hints on how to continue please?

So normally would it be zero order as the offspring at each stage are independent of the any offspring around them in the same generation. "By conditioning on the value of X1, and then thinking of future generations as a particular generation of the separate branching processes spawned by...

In particular could someone explain what it is saying when it says "By conditioning on the value of X1, and then thinking of future generations as a particular generation of the separate branching processes spawned by these children" I think this is essentially the key but I don't understand...

Could you explain further, after reconsideration I know for sure my original working was totally incorrect. Could anyone help me out? Possibly start me off? Thanks.

By conditioning on the value of X1, and then thinking of future generations as a particular generation of the separate branching processes spawned by these children, show that Fn(s), defined by Fn(s) = E(s^Xn), satisfies Fn(s) = F(Fn−1(s)) ∀n ≥ 2. I need to prove the above result and...

So is that all correct now? Also thank you so much for all the help!

Would this work? A={(a,b,c,d,0,e,f,g,h,0)} B={(a,0,b,c,d,e,f,g,h,i)} Then A and B span R^10 since a linear combiantion Q(a,b,c,d,0,e,f,g,h,0) + P(a,0,b,c,d,e,f,g,h,i) = (Qa+Qb,Qb,Qc+Pb,...) = (x1,x2,x3,x4,x5,x6,x7,x8,x9,x10). And also A∩B i think is equal to {(a,0,b,c,0,d,e,f,g,0). Is that...

I'm not getting very far, could you give another hint perhaps? Thanks.

For the answer of 7 would the following be okay? A={(a,b,0,c,d,e,f,g,0,h) |a,b,c,d,e,f,g,h are Real} B={(a,b,0,c,d,e,f,g,h,i) |a,b,c,d,e,f,g,h,i are Real} Then dim A = 8, dim B = 9, but A∩B = ({a,b,0,c,d,e,f,g,0,0)|a,b,c,d,e,f,g are Real} and this has dimension 7? Also going back to my earlier...

Does it not need to equal 7? As my answer before was dim(A∩B) = 7 or 8, not 8 or 9?

Would it equal to dim(A) and so 8?