1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the ideal generated by a and b.

  1. Sep 3, 2008 #1
    what is "the ideal generated by a and b."

    I'm doing a problem and I'm a little confused on the notation.

    Let R be a ring and [tex]a,b \in R[/tex]. Prove that [tex](a, b)[/tex], the ideal generated by a and b is the...

    I want to do this on my own so I left out the rest of the problem. I just need to know if [tex](a, b) = aR \cup bR[/tex]. Or is it some kind of set of ordered pairs?
     
  2. jcsd
  3. Sep 3, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: what is "the ideal generated by a and b."

    It's not the union aR and bR. It's the set of all sums of the form aR+bR. They aren't the same. And unless (a,b) is some funny notation different from {a,b} then it has nothing to do with ordered pairs.
     
  4. Sep 3, 2008 #3
    Re: what is "the ideal generated by a and b."

    Okay that makes sense. The way I described it it wouldn't even be closed under addition.
     
  5. Sep 5, 2008 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Re: what is "the ideal generated by a and b."

    General remark: Usually the phrase "object of type T generated by a set X" means "smallest object of type T containing the set X." And usually this is the 'intersection' (or appropriate analogue) of all objects of type T containing the set X.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is the ideal generated by a and b.
Loading...