 [SOLVED] Ring theory  

Author  Message 

Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: [SOLVED] Ring theory Thu Nov 12, 2009 12:09 am  
 I hope the translation is not vague! Poor marker first gave me 8/20 till I had to point the details lost in the computations and then he gave 20/20 right away My 60 seconds problem: uploading.com ring.pdf/ 

 
Jim Pythagoras
Posts : 17 Join date : 20091109
 Subject: Re: [SOLVED] Ring theory Tue Nov 17, 2009 5:06 pm  
 So this problem is supposed to take 60 seconds. I don't see it, but my memory of basic ring theory isn't as good as it should be. I'm going to work on this problem some more tonight. 

 
Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: Re: [SOLVED] Ring theory Tue Nov 17, 2009 5:17 pm  
 No, it is supposed to take 60 seconds to be downloaded not to be solved and in fact you just need to use your basic memories. 

 
Jim Pythagoras
Posts : 17 Join date : 20091109
 Subject: Re: [SOLVED] Ring theory Tue Nov 17, 2009 5:33 pm  
 Okay I don't feel so bad now. 

 
Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: Re: [SOLVED] Ring theory Tue Nov 17, 2009 5:51 pm  
 Jim, It is great that you are interested in solving problem section, I put 10$ prize for this problem I hope you make it tonight 

 
Bruno Admin
Posts : 184 Join date : 20090915 Age : 30 Location : the infinite, frictionless plane of uniform density
 Subject: Re: [SOLVED] Ring theory Tue Nov 17, 2009 5:53 pm  
 

 
Jim Pythagoras
Posts : 17 Join date : 20091109
 Subject: Re: [SOLVED] Ring theory Wed Nov 18, 2009 11:19 am  
 Gaah I thought I had this problem last night but then I looked at the definition of nilpotent this morning and saw that I need to show that I is a nilpotent ideal if and only if there exists a natural number k such that the product of any k elements of I is 0, not just a product of the same element. Then I realized that I was not being general enough in what an element of the two sided ideal I constructed looked like so now I don't really think I got anywhere. 

 
Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: Re: [SOLVED] Ring theory Wed Nov 18, 2009 4:32 pm  
 Hey, Jim you should be close, in this case knowing that $x^2=0$ gives many information and let's say everything! One of the most important nilpotent ideal in R is N(R)={x; Rx=0} for which obviously we have $N(R)^2=0$ so by assumption we get $N(R)=0$. Now the rest of the proof lies on using this fact repeatedly. I'll post solution at this weekend. 

 
peyman Euclid
Posts : 49 Join date : 20091106 Age : 94 Location : dense in the universe
 Subject: Re: [SOLVED] Ring theory Wed Nov 18, 2009 10:38 pm  
 I know almost nothing about rings. Do you have a reference to a short introduction? 

 
Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: Re: [SOLVED] Ring theory Wed Nov 18, 2009 10:47 pm  
 Personally I am a big fan of Basic abstract algebra by Bhattacharya, though it has a bit of ring theory but develop your skill in dealing with rings so much I love this book. 

 
Jim Pythagoras
Posts : 17 Join date : 20091109
 Subject: Re: [SOLVED] Ring theory Thu Nov 19, 2009 11:14 am  
 My personal preference for an introduction is Dummit and Foote Abstract Algebra. (I don't know if they have it here but chapters 7, 8, 9 are good.)
There are also books by Lam that are more advanced. Introduction to Noncommutative Ring Theory which is a GTM Springer book and it has a problem book to accompany it Problems in Ring Theory. I have tried to do a few of the problems in the book but I was never very good at them because I didn't have very good intuition. 

 
Mohammad Descartes
Posts : 100 Join date : 20091105 Age : 34 Location : Right behind you
 Subject: Sol Sat Nov 21, 2009 8:16 pm  
 

 
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 Subject: Re: [SOLVED] Ring theory  
 

 
 [SOLVED] Ring theory  
