Standard Lemma guide

commutative

adj · 5 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

adj

Meaning 1

Such that the order in which the operands are taken does not affect their image under the operation.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematics, sciences

Examples

  • Addition on the real numbers is commutative because for any real numbers s,t, it is true that s#43;t#61;t#43;s.
  • Addition and multiplication are commutative operations but subtraction and division are not.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

adj

Meaning 2

Having a commutative operation.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

adj

Meaning 3

Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

4

adj

Meaning 4

Relating to exchange; interchangeable.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

5

adjective satellite

Meaning 5

(of a binary operation) independent of order; as in e.g.

Definition source: Princeton WordNet 3.0

Examples

  • a x b = b x a

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From French commuter (“to substitute or switch”) + -ative (“tending to”). See commute.

Across languages

Translations

34 source translations are retained for this English entry.

  • Catalan: commutatiu — mathematics: such that order of operands does not affect result
  • Chinese Mandarin: 可交換的 /可交换的 — mathematics: such that order of operands does not affect result
  • Czech: komutativní — mathematics: such that order of operands does not affect result
  • Danish: kommutativ — mathematics: such that order of operands does not affect result
  • Dutch: commutatief — mathematics: such that order of operands does not affect result
  • Esperanto: komuta — mathematics: such that order of operands does not affect result
  • Finnish: kommutatiivinen — mathematics: such that order of operands does not affect result
  • Finnish: vaihdannainen — mathematics: such that order of operands does not affect result
  • French: commutatif — mathematics: such that order of operands does not affect result
  • German: kommutativ — mathematics: such that order of operands does not affect result
  • Greek: αντιμεταθετικός (antimetathetikós) — mathematics: such that order of operands does not affect result
  • Hindi: विनिमेय (vinimey) — mathematics: such that order of operands does not affect result
  • Icelandic: víxlinn — mathematics: such that order of operands does not affect result
  • Indonesian: komutatif — mathematics: such that order of operands does not affect result
  • Italian: commutativo — mathematics: such that order of operands does not affect result
  • Polish: przemienny — mathematics: such that order of operands does not affect result
  • Portuguese: comutativo — mathematics: such that order of operands does not affect result
  • Romanian: comutativ — mathematics: such that order of operands does not affect result
  • Russian: коммутативный (kommutativnyj) — mathematics: such that order of operands does not affect result
  • Russian: перестановочный (perestanovočnyj) — mathematics: such that order of operands does not affect result
  • Tagalog: palitin — mathematics: such that order of operands does not affect result
  • Turkish: değişmeli — mathematics: such that order of operands does not affect result
  • Catalan: commutatiu — algebra: having a commutative operation
  • Chinese Mandarin: 可交換的 /可交换的 — algebra: having a commutative operation
  • Czech: komutativní — algebra: having a commutative operation
  • Esperanto: komuta — algebra: having a commutative operation
  • Finnish: kommutatiivinen — algebra: having a commutative operation
  • Finnish: vaihdannainen — algebra: having a commutative operation
  • German: kommutativ — algebra: having a commutative operation
  • Indonesian: komutatif — algebra: having a commutative operation
  • Portuguese: comutativo — algebra: having a commutative operation
  • Romanian: comutativ — algebra: having a commutative operation
  • Tagalog: palitin — algebra: having a commutative operation
  • Turkish: değişmeli — algebra: having a commutative operation
Real reading context

commutative in complete knowledge articles