Montreal Math Club

Mathematics students in Montreal - Étudiants de mathématiques à Montréal
 
HomeHome  CalendarCalendar  FAQFAQ  SearchSearch  MemberlistMemberlist  UsergroupsUsergroups  RegisterRegister  Log in  

Share | 
 

 [SOLVED] Ring theory

Go down 
AuthorMessage
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

PostSubject: [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 Very Happy
My 60 seconds problem: uploading.com ring.pdf/
Basketball
Back to top Go down
View user profile
Jim
Pythagoras
Pythagoras
avatar

Posts : 17
Join date : 2009-11-09

PostSubject: 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.
Back to top Go down
View user profile
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

PostSubject: 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 Very Happy
and in fact you just need to use your basic memories.
Back to top Go down
View user profile
Jim
Pythagoras
Pythagoras
avatar

Posts : 17
Join date : 2009-11-09

PostSubject: Re: [SOLVED] Ring theory   Tue Nov 17, 2009 5:33 pm

Okay I don't feel so bad now.
Back to top Go down
View user profile
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

PostSubject: 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 Very Happy
I hope you make it tonight Basketball
Back to top Go down
View user profile
Bruno
Admin
avatar

Posts : 184
Join date : 2009-09-15
Age : 31
Location : the infinite, frictionless plane of uniform density

PostSubject: 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 Very Happy
I hope you make it tonight Basketball

Yes, now we are three! cheers

Now I'm wary of all problems with a prize though. geek
Back to top Go down
View user profile http://mathclub.justforum.net
Jim
Pythagoras
Pythagoras
avatar

Posts : 17
Join date : 2009-11-09

PostSubject: 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.
Back to top Go down
View user profile
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

PostSubject: 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.
Back to top Go down
View user profile
peyman
Euclid
Euclid
avatar

Posts : 49
Join date : 2009-11-06
Age : 94
Location : dense in the universe

PostSubject: 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?
Back to top Go down
View user profile
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

PostSubject: 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 Very Happy
I love this book. bounce
Back to top Go down
View user profile
Jim
Pythagoras
Pythagoras
avatar

Posts : 17
Join date : 2009-11-09

PostSubject: 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.
Back to top Go down
View user profile
Mohammad
Descartes
Descartes
avatar

Posts : 100
Join date : 2009-11-05
Age : 34
Location : Right behind you

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

Back to top Go down
View user profile
Sponsored content




PostSubject: Re: [SOLVED] Ring theory   

Back to top Go down
 
[SOLVED] Ring theory
Back to top 
Page 1 of 1

Permissions in this forum:You cannot reply to topics in this forum
Montreal Math Club :: Mathematics :: Problem Solving :: Solved problems-
Jump to: