Re: Does commutativity imply associativity?
From: G. A. Edgar (edgar_at_math.ohio-state.edu.invalid)
Date: 08/27/04
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Date: Fri, 27 Aug 2004 19:03:59 -0400
In article <12f59340.0408271435.4abe582c@posting.google.com>, Brian Smith <brianscsmith@yahoo.com> wrote:
> I know that there are mathematical objects which are associative but
> not commutative with respect to some binary operation. Matrix
> multiplication is an example, associative but not commutative.
>
> My question is: Is there some set of objects which is commutative but
> not associative with respect to some binary operation, or does
> commutativity imply associativity?
Practically anything you can think of.
Lets define x % y = 2x + 2y .
It's commutative, right?
But is it associative?
x % (y % z) = 2x + 4y + 4z ,
(x % y) % z = 4x + 4y + 2z ,
not equal in general.
-- G. A. Edgar http://www.math.ohio-state.edu/~edgar/
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