Verify that if A is an Abelian group, with addition as operation, and an operation * is defined on A by a*b=0 for all a,b E A, then A is a ring with respect to + and *.
Can anybody offer any advice on solving this problem please?
Verify that if A is an Abelian group, with addition as operation, and an operation * is defined on A by a*b=0 for all a,b E A, then A is a ring with respect to + and *.
Can anybody offer any advice on solving this problem please?
Thanks.
well, it is given that <A,+> is abelian.. you only have to check two properties.. (associativity of *) a*(b*c)=(a*b)*c and (DPMA) a*(b+c)=a*b + a*c for all a,b,c in A..