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You are not logged in. #1 20090104 05:55:27#2 20090104 07:16:17
Re: Frobenius endomorphismThis theorem, which I have always heard as the "freshman calculus theorem", says that: This property has important implications in Field theory and Galois theory. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20090104 07:27:06
Re: Frobenius endomorphismIt’s a neat result. By the way, the definition requires the characteristic of the ring to be prime. What if the characteristic is a nonprime positive integer? will still be a homomorphism, won’t it? #4 20090104 08:49:18
Re: Frobenius endomorphismThis theorem as I mentioned previously is mostly used in field and Galois theory (in my experience). As such, we are always talking about integral domains and with any integral domain, the characteristic is always prime or 0 (i.e. infinite). Last edited by Ricky (20090104 08:54:37) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20090104 08:52:46#6 20090104 09:57:21
Re: Frobenius endomorphismI would like someone to check my work if possible, but here's what I have so far. These are all found by expanding (1+1)^n, (p*1 +1)^n, and (q*1+1)^n by the binomial theorem. What I find rather interesting is that (p*1 + q*1)^n = (p*1)^n + (q*1)^n, again found by expanding the binomial theorem. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 