Question

Modern Algebra: Is S={a,b|a+b=0} a subring of Z x Z? Justify.

Answer 1

I think it's false but I don't know why :(

Answer 2

is (-1,1) in S?

Answer 3

Someone told me it was closed under multiplication which is what I'm having trouble understanding.

Answer 4

Also (-1,1) is in Z.

Answer 5

what is (-1,1)*(-1,1)

Answer 6

(-1,1) is in \(Z\times Z\)

Answer 7

what is (-1,1)*(-1,1)

Answer 8

(1,1)

Answer 9

is (1,1) in S?

Answer 10

I guess 1 is not equal to 0 so no?

Answer 11

correct....you have your answer ;)

Answer 12

Oh, well thank you!