Subrng

A subrng is a subset of a rng $𝑆 \subseteq 𝑅$ such that $𝑆$ is a ring under the same operations, ring i.e. $𝑆$ forms both a subgroup under addition and subsemigroup under multiplication of $𝑅$ .

Subrng test

Theorem. Iff $𝑎 - 𝑏$ and $𝑎 𝑏$ are in $𝑆$ whenever $𝑎, 𝑏 \in 𝑆$ , then $𝑆$ is a subrng of $𝑅$ . ring

Proof

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

tidy | en | SemBr

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Subrng

Subrng test

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