My Math Forum Little question about the field axioms

 Abstract Algebra Abstract Algebra Math Forum

 February 19th, 2011, 04:07 AM #1 Member   Joined: Nov 2010 Posts: 34 Thanks: 0 Little question about the field axioms Hi! I have seen that in proofs, they often omit several of the field axioms. In fact, they usually just show that the set and the operator is closed under addition, subtraction, multiplication and division and the rest of the axoims sort of magicaly follows. I think there is some result that allow one to do this (As I have mentioned in earlier posts). I have gone over my book several times, but for some reason I still cannot find the reason. I would be very happy if someone could help me.
 February 19th, 2011, 04:59 AM #2 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: Little question about the field axioms If you have a subset of field, then most of the field axioms are inherited. For example the real numbers form a field. So to check that the rational numbers form a field you need only check the various closures, and that 0 and 1 are in the set.
 February 20th, 2011, 01:52 AM #3 Member   Joined: Nov 2010 Posts: 34 Thanks: 0 Re: Little question about the field axioms Ok, I see. Thanks a lot.

 Tags axioms, field, question

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post krausebj0 Number Theory 0 June 28th, 2013 07:01 AM watson Abstract Algebra 1 September 14th, 2012 10:07 PM Hooman Real Analysis 5 November 29th, 2011 05:38 AM Touya Akira Abstract Algebra 2 February 23rd, 2011 01:06 AM Touya Akira Abstract Algebra 3 February 7th, 2011 05:50 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top