What does "subring" mean?

A ring which is contained in a larger ring, such that the multiplication and addition on the former are a restriction of those on the latter. When rings are required to have a multiplicative identity (as is standard in most branches of algebra), the subring must also have the same multiplicative identity as the larger ring.

Subring

//ˈsʌbˌɹɪŋ// noun

noun ·Rare ·Advanced level

Definitions

Noun

1
A ring which is contained in a larger ring, such that the multiplication and addition on the former are a restriction of those on the latter. When rings are required to have a multiplicative identity (as is standard in most branches of algebra), the subring must also have the same multiplicative identity as the larger ring.

Etymology

From sub- + ring.

Related phrases

prime subring

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.