Commutative ring with unit

1. Sep 7, 2008

fk378

1. The problem statement, all variables and given/known data
Given a set R={x,y,a,b}

There are 2 tables shown: one is the addition of x,y,a,b elements with x,y,a,b elements. The 2nd table is multiplication of each element with the other elements. (The 2nd table shows that x multiplied by anything equals x)

we have a+b=y and (a)(b)=y

Decide which elements must be the 0 and the 1, then prove that this is a commutative ring with unit.

3. The attempt at a solution
I know how to show it is commutative. I'm just having trouble starting on it.

Well if the addition of a and b equals the multiplication of a and b, then a=b=y=0. Is this right? But then since x multiplied by anything equals x, then x must also be 0. But then there is no element 1. So how can I show commutativity with this??

Also don't know how to show that there exists units.

Last edited: Sep 7, 2008
2. Sep 8, 2008

tiny-tim

Hi fk378!

It would help if you showed us the table …

either use the code tag like this…

Code (Text):
a b c d
e f g h
i j k l
m n o p
or use LaTeX and http://www.physics.udel.edu/~dubois/lshort2e/node56.html#SECTION00850000000000000000 [Broken]

Last edited by a moderator: May 3, 2017