# Early Abstract Algebra Problem - Pinter's Textbook

1. Aug 11, 2012

### physicsforum7

1. The problem statement, all variables and given/known data
This problem is from Charles C. Pinter's A Book of Abstract Algebra, Second Edition. The problem is B7 of Chapter 2.

Show that the operation * is either associative or not.

x*y=$\frac{xy}{x+y+1}$

This problem seems simple to me: I keep arriving at YES for an answer; more specifically,

x*(y*z)=(x*y)*z=$\frac{xyz}{xy+xz+yz+x+y+z+1}$.

However, the solution in the back claims that the answer is NO, the operation is not associative. More specifically,

x*(y*z)=$\frac{xyz(y+z+1)}{xy+xz+yz+x+y+z+1}$.

(x*y)*z= $\frac{xyz(x+y+1)}{xy+xz+yz+x+y+z+1}$.

After working the problem through several times, I'm pretty sure this is a mistake in the book. But I would greatly appreciate feedback so that I can be sure I'm not doing something terribly wrong.

Thank you very much.

2. Aug 11, 2012

### micromass

Staff Emeritus
I agree with you. The operation seems to be associative.

3. Sep 19, 2012

### funwalla

I also get the same result.

4. Sep 19, 2012

### HallsofIvy

Staff Emeritus
But surely your text does not "Show that the operation * is either associative or not."
Every operation is "either associative or not"!

Better wording would be "Determine whether the operation * is either associative or not."