Recent content by tinynerdi

I have the same problem. How would do you symmetric and transitive? Do you suppose to use integral?

Homework Statement let F be a field and f(x),g(x) in F[x]. Show that f(x) divides g(x) if and only if g(x) in <f(x)> Homework Equations let E be the field F[x]/<f(x)> The Attempt at a Solution <=> if f(x) divides g(x) then g(x) in <f(x)> Proof: Suppose f(x) divides g(x)q(x). then...

it is R?

Homework Statement how that N is a maximal ideal in a ring R if and only if R/N is a simple ring. that is it is nontrivial and has no proper nontrivial ideals. Homework Equations The Attempt at a Solution I don't know how to start. Please help.

Can we just state that because Tv=0 iff and -Tv = 0 therefore N((T-λI)^k) = N((λI-T)^k) or do we have to prove that Tv=0 iff and -Tv = 0?

Yeah, that is what I am trying to prove.

Homework Statement Let T:V->W be a linear transformation. Prove that if V=W (So that T is linear operator on V) and λ is an eigenvalue on T, then for any positive integer K N((T-λI)^k) = N((λI-T)^k) Homework Equations T(-v) = -T(v) N(T) = {v in V: T(v)=0} in V hence T(v) = 0 for all...

I forgot about that.. let try Z/ZxZ =~ Z Since ZxZ is a subring of Z.

Homework Statement give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain. Homework Equations since we know that ZxZ is a zero divisor and 5Z is an integral domain. The Attempt at a Solution So, ZxZ/5Z =~(isomorphic to) Z/5Z=~ Z_5.