Question #35f5d

1 Answer
Oct 22, 2016

No

Explanation:

A ring must contain a multiplicative identity. As there is only one such element 1_R1R in RR, and TT is a restriction of RR with the same operations, then the only possible multiplicative identity for TT is 1_R1R.

However, as n > 0n>0, we have n*1_R = n != 0n1R=n0. Thus 1_R !inT1RT, meaning TT has no multiplicative identity and thus cannot be a ring (or subring).