Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i.(adsbygoogle = window.adsbygoogle || []).push({});

A lemma that is not proven is given. If xy_{i}=1_{R}& y_{j}x=1_{R}, then y_{i}=y_{j}

I need to show that y_{j}x=1R.

Right now I haven't got much. I took the contrapositive of the lemma, but I still get stuck as I'm not sure where I could go from there with the information that I'm given.

The book gives a theorem which states Let R be a ring with identity and a, b of R. If a is a unit each of the equations ax=b & ya=b has a unique solution in R.

Then it goes on to state that if the ring is not commutative, x may not be equal to y. But yeah, I'm still stuck.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Abstract Proof

**Physics Forums | Science Articles, Homework Help, Discussion**