Abstract Algebra problem Please show your work clearly If w

Abstract Algebra problem - Please show your work clearly!

If we are working within a Ring, prove that a in the Ring.

Solution

R is a ring

The binary operations are addition and multiplication..

( R +) is an abelian group w.r.t addition

0,the additive identity is in R

For all a in R,we have

1. 0+0a=0a=(0+0)a=0a+0a. By the cancellation law it now follows that 0a=0