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An undergraduate course in Abstract Algebra Course notes for ...
iv)
a0
0 =
a0
(Axiom (i))= a(0 0) (Axiom (ii))=
a0
a0
(Axiom (vi)). ... By part (i) above it follows that
a0
= 0. The proof that 0a = 0 is similar.
www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf
1