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!

Binary Operation

  1. Nov 13, 2005 #1
    How is multiplication in [tex]R=\mathbb{Z}_5 \times \mathbb{Z}_5[/tex] defined? if (a,b) and (c,d) is in R, what's (a,b)(c,d)? (ac,bd)?
     
  2. jcsd
  3. Nov 13, 2005 #2
    Usually pointwise (i.e. (a, b)(c, d) = (ac, bd) as you guessed). It can easily be extended to other groups (rings).
     
  4. Nov 13, 2005 #3
    What do you mean by extending to other rings? I'm trying to find an isomorphism between Z5XZ5 and Z5[x]/X^2+1 and am having a hard time finding it. If I can redefine multiplication in Z5XZ5 then it will be easy.
     
  5. Nov 13, 2005 #4
    I mean that given any rings G, H, you can easily define the product ring GxH in the same (pointwise) fashion.

    I doubt the author (unless he or she said otherwise) intended for you to redefine Z_5 x Z_5.

    Given any polynomial p, there are unique constants a, b and a polynomial q such that

    p(x) = q(x)(x^2 + 1) + ax + b.

    There seems to be an obvious function between Z_5[x]/(x^2 + 1) and Z_5 x Z_5 to try. But I haven't myself.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Binary Operation
  1. Binary operation (Replies: 5)

  2. Binary operations (Replies: 1)

Loading...