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 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= (1-r^(n+1) / (1-r) 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
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Math Focus: Number Theory
Re: ring fraction.

Quote:
 Originally Posted by sebaflores 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= (1-r^(n+1) / (1-r)
Too complicated, can be false too, I haven't checked.

Try using the fact that r is a zero-divisor if a * r of r * b is 0 for some non zero a, b in R. So, what if r is not a zero-divisor? Can you formally state what is the definition of an element that is not a zero-divisor? Tags fraction, ring Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ThePope Elementary Math 3 November 4th, 2012 06:05 AM daigo Algebra 3 July 15th, 2012 01:05 AM Tommy_Gun Algebra 5 June 3rd, 2012 06:14 PM Joolz Abstract Algebra 0 October 18th, 2011 09:29 AM cosette Abstract Algebra 5 January 16th, 2009 04:08 AM

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