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 Post subject: Examples of RingsPosted: Fri, 4 May 2012 03:05:13 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
So here's the problem: In each of the following, a set A w/ operations addition and multiplication is given. Prove that A satisfies all the axioms to be commutative ring w/unity. Indicate the zero element, the unity and the negative of an arbitrary a.
1.) A is the zet of Z of integers with the following "addition" + and "multiplication" x:

a+b=a+b+1 ; axb=ab-(a+b)+2.

So i worked it out but my teacher said i need to show the distributive property?

do i have to multiply by an x, like x(a+b+1) and x((a+b)+2)?

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 Post subject: Re: Examples of RingsPosted: Fri, 4 May 2012 16:29:14 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12165
Location: Austin, TX
DgrayMan wrote:
So here's the problem: In each of the following, a set A w/ operations addition and multiplication is given. Prove that A satisfies all the axioms to be commutative ring w/unity. Indicate the zero element, the unity and the negative of an arbitrary a.
1.) A is the zet of Z of integers with the following "addition" + and "multiplication" x:

a+b=a+b+1 ; axb=ab-(a+b)+2.

So i worked it out but my teacher said i need to show the distributive property?

do i have to multiply by an x, like x(a+b+1) and x((a+b)+2)?

Then you need to show that and if you have shown commutativity of that's enough, if not, you also need to show

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