Recent content by joecoz88

Hello, Let [a,b] be the ideal generated by a and b. If R is a commutative ring with unity, let a be in R and m,n be natural numbers. Show that [ (a^m)-1, (a^n)-1 ] = [ (a^gcd(m,n)) -1 ] Seems simple but I am having trouble with it. Thanks in advance!

Kernel <--> Ideal? I know that all kernels of ring homomorphisms are ideals, but is it true that for any ideal I of a ring R, there exists a homomorphism f: R -> R' such that Ker(f)=I?

Thank you so much for the response. My next question is, must S be a subring of Z? Can one obtain all localizations of Z by localizing with all of its subrings? Also, what form do these localizations take? I am assuming there is a general one. For example, {(n/p^k) : n, k in Z, p prime}...

What are the localizations of Z? I'm having trouble understanding what localization is.

Yes I see that my solution wasn't general enough, thanks for the correction. But I am having trouble following quasars logic, maybe someone could elaborate? I can't see the reason why if 2Z and 3Z are isomorphic, then Z/2Z and Z/3Z should be isomorphic? Is this reasoning valid? As...

Consider the isomorphism that relates 2Z and 3Z as abelian groups (or nZ for any integer n). As groups, these structures are isomorphic. In order to be isomorphic as rings, the homomorphism property must be satisfied for addition and multiplication. We know that addition works, and we need to...

Yeah it is the first one, "Principles of Mathematical Analysis." Here is the course description, though its probably not completely accurate: The real number system. Sequences, limits, and continuous functions in R and 'Rn'. The concept of a metric space. Uniform convergence, interchange...

Thanks for the replies. I am a pure math major and I have already taken linear and abstract algebra, and I am going on to real analysis and Galois theory next semester. The reason I asked the question is because I have noticed that as my skills in upper division (proof based) mathematics...

Learning Real Analysis --> Calculus Hello, Just a quick question I am wondering about. I am going to take my first real analysis course next semester using Rudin. Obviously I have already gone through the usual calculus sequence. I am wondering if learning real analysis will help...

Hello I am currently a pure math major at a top level university, and I am basically committed to attending grad school. I am in my junior year right now. I am planning on taking several graduate courses as electives during my senior year. My question is whether I should apply to grad...

Working in Sn, define a bijection from An to Bn, where Bn is the set of all odd permutations. f: An -> Bn f(x)=yx where y is in Bn You can easily show this map is a bijection, therefore An and Bn have the same cardinality. So exactly half of the permutations in Sn are even ( and the...

Does anybody know of any good websites that contain a clear proof of the existence of the Jordan Canonical Form of matrices? My professor really confused me today

Homework Statement If G is a finite group that has exactly one subgroup H of a given order, then H is normal. Homework Equations N/A The Attempt at a Solution I cannot figure out what makes a subgroup H special if it is the only one of a given order...

I have been struggling with this proof: If G is a finite group with exactly one subgroup H of a given order, then H is normal. I'm not sure where to start...