Question #35f5d

1 Answer
sente
Oct 22, 2016

No

Explanation:

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

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

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