a) Show that
is a commutative ring
b) Show that if
then
and
Answers
a) Is it sufficient to show that
satisfies additive commutative, associativity, identity and inverse and satisfies multiplicative associativity, commutativity and identity?
In that case
Noting that
is a commutative ring
Additive commutativity
The above statements are equal to each other, then
satisfies this property.
Multiplicative commutativty
Above 2 expressions are equal to each other, then
satisfies this property.
Do I continue in this vein with the other properties to prove that
is a commutative ring?
Part B
Is it sufficient to show that
This
and
Hence
and
Will this suffice?
Thanks for the responses in advance