When you analyse an algebraic division Ring, a set E with with 2 operations called '+' and '*' with the axioms of the algebraic goup (E.+) previously proven with commutivity a+b = b+a, the exitence of one element we called 0 where for all x in E: x+0 = x, with the set not being empty or singular;
Given the properties of the operation '*':
1: there exists a member we call u where for all set members a, a*u = a
2: for all members of E, a*b = b*a
3: for all a,b,c in E, a*(b+c) = a*b+a*c
With these in mind prove that a*0=0 and while you're at it prove that 0 is not equal this 'u' mentioned on the axioms.
Given the properties of the operation '*':
1: there exists a member we call u where for all set members a, a*u = a
2: for all members of E, a*b = b*a
3: for all a,b,c in E, a*(b+c) = a*b+a*c
With these in mind prove that a*0=0 and while you're at it prove that 0 is not equal this 'u' mentioned on the axioms.