Phrase guide

local ring

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal.

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • The unique maximal ideal of a (commutative) local ring contains all of the zero divisors of such ring, and all elements of the ring outside of it are units. Then in a local ring, the sum of any two zero divisors is also a zero divisor. Contrapositively, if two ring elements add up to a unit then one of them must be a unit as well. A simple example of a local ring is #92;mathbb#123;Z#125;#95;8.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Narrower terms: simple ring, field

2

noun

Meaning 2

The non-routing segment of a token ring network.

Definition source: English Wiktionary via Wiktextract

Topics: computing, engineering, mathematics, natural-sciences, networking, physical-sciences, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.