Prove that for all a,b in a ring R,

The hint says use:

Since any integer has a negative, we know

Multiple by b:

How can I show from the above?

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- Jul 6th 2011, 08:57 AMdwsmithProve that for all a,b in a ring R, (-a)b=-ab=a(-b)
Prove that for all a,b in a ring R,

The hint says use:

Since any integer has a negative, we know

Multiple by b:

How can I show from the above? - Jul 6th 2011, 10:05 AMChris L T521Re: Prove that for all a,b in a ring R, (-a)b=-ab=a(-b)
Interesting approach (I don't have a problem with it). Note that . So the first part follows right away: .

For the second part, you do pretty much the same thing; however, you start with and then multiply by on the left:

Then because '=' is transitive, it now follows that .

I hope this makes sense. - Jul 6th 2011, 10:26 AMIsomorphismRe: Prove that for all a,b in a ring R, (-a)b=-ab=a(-b)