Subrng

A subrng is a subset of a rng such that is a ring under the same operations, #m/def/ring i.e. forms both a subgroup under addition and subsemigroup under multiplication of .

Subrng test

Theorem. Iff and are in whenever , then is a subrng of . #m/thm/ring

Proof

The One step subgroup test tests for the additive subgroup, whereas closure is necessary and sufficient for multiplication.

#state/tidy | #lang/en | #SemBr