
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 20th, 2012, 04:55 AM  #1 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  maximal ideal of the ring Q trivial question??
I am supposed to give an example or a counterexample: Claim: If is a ring homomorphism then takes maximal ideals of B to maximal ideals of A. Solution: If I let now I have an injective and surjective ring homomorphism ,and my question is why is a maximal ideal in ??? We know that which is NOT a maximal ideal in as f.ex giving a counterexample. Maybe it is a trivial question but I just don't see it....Please help 
November 20th, 2012, 11:03 AM  #2 
Senior Member Joined: Aug 2010 Posts: 195 Thanks: 5  Re: maximal ideal of the ring Q trivial question??
We know that is a field. In any field, any nonzero element is a unit, so any ideal with nonzero elements must have units, hence must have 1. Any ideal containing 1 is the whole ring, so any nonzero ideal of a field is the entire field. Therefore the (unique) maximal proper ideal of any field is the zero ideal.

November 21st, 2012, 03:16 AM  #3 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  Re: maximal ideal of the ring Q trivial question??
Of course you are right I totally forgot about it. thank you 

Tags 
ideal, maximal, question, ring, trivial 
Search tags for this page 
Maximal ideal of Q,ideal ring q,how to check maximal ideal in Q,ideals of q by q,maximal ideals of q,the ideal (0) is maximal in Q [i],ideal (0) is maximal ideal in Q[i],QĂ—Q maximal ideal,maximal ideals of Q ?,wht is trivialideal,ideal in q,maximal ideal trivial,Maximal ideal in Q,maximal ideal ex,maximales ideal in q
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Maximal ideal  limes5  Abstract Algebra  7  January 6th, 2014 03:43 PM 
maximal ideal  cummings123  Abstract Algebra  1  February 27th, 2013 05:06 AM 
Ideal Proof, possibly a trivial question  HairOnABiscuit  Abstract Algebra  2  October 4th, 2012 08:08 PM 
ideal and maximal  silvi  Abstract Algebra  2  January 20th, 2010 03:05 AM 
Maximal Ideal  julien  Abstract Algebra  1  November 19th, 2006 05:56 PM 