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# [SOLVED] Ring theory

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Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
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/

Pythagoras

Posts : 17
Join date : 2009-11-09

 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.

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
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.

Pythagoras

Posts : 17
Join date : 2009-11-09

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

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
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

Posts : 184
Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Ring theory   Tue Nov 17, 2009 5:53 pm Mohammad wrote: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 Yes, now we are three! Now I'm wary of all problems with a prize though.

Pythagoras

Posts : 17
Join date : 2009-11-09

 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.

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
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 nil-potent 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.

Euclid

Posts : 49
Join date : 2009-11-06
Age : 95
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?

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
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, thoughit has a bit of ring theory but develop your skill in dealing with rings so much I love this book.

Pythagoras

Posts : 17
Join date : 2009-11-09

 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.

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: Sol   Sat Nov 21, 2009 8:16 pm

 Subject: Re: [SOLVED] Ring theory

 [SOLVED] Ring theory
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