November 22nd, 2013, 08:49 AM  #1 
Newbie Joined: Sep 2013 Posts: 17 Thanks: 0  ring fraction.
If r in R a non empty element such that is not a zero divisor . Prove that is not a zero divisor with n in N.

November 22nd, 2013, 09:05 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: ring fraction.
Can you prove that the same is true for r^2? Then inductively apply for the rest of the exponents?

November 25th, 2013, 05:11 AM  #3 
Newbie Joined: Sep 2013 Posts: 17 Thanks: 0  Re: ring fraction.
I'm not sure, but If r is a real number not equal to 1, then for every n>=0 , then , r^0 + r^1 +......+r^n= (1r^(n+1) / (1r) if you consider this? is valid? Now , how i use the hypotesis ? : If r in R a non empty element such that is not a zero divisor I dont understand 
November 25th, 2013, 05:46 AM  #4  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: ring fraction. Quote:
Try using the fact that r is a zerodivisor if a * r of r * b is 0 for some non zero a, b in R. So, what if r is not a zerodivisor? Can you formally state what is the definition of an element that is not a zerodivisor?  

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