Word.ws English Dictionary

commutative ring

commutative ring noun: a ring whose multiplicative operation is commutative.

Noun

commutative ring (plural commutative rings)

  1. (ring theory) A ring whose multiplicative operation is commutative.
    • Among commutative rings, the polynomial rings in a finite number of indeterminates enjoy important special properties and are frequently used in applications.1960, Oscar Zariski, Pierre Samuel, Commutative Algebra II, Springer, page 129
    • As usual, it is simpler to begin by looking at a more general setting—in this case, commutative rings—before getting involved with polynomial rings. It turns out that the nature of the ideals in a commutative ring is important: for example, we have already seen that gcd's exist in PIDs, while this...2002, Joseph J. Rotman, Advanced Modern Algebra, 2nd edition, American Mathematical Society, page 295

commutative ring meaning in Tamil

commutative ring in Tamil

பரிமாற்று வளையம்

Examples of commutative ring in a sentence

  • As usual, it is simpler to begin by looking at a more general setting—in this case, commutative rings—before getting involved with polynomial rings.2002, Joseph J. Rotman, Advanced Modern Algebra, 2nd edition, American Mathematical Society, page 295:
  • In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.2004, K. R. Goodearl; R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, page 47:

Forms of commutative ring

pluralcommutative rings

Questions about commutative ring

What does commutative ring mean?
Commutative ring means a ring whose multiplicative operation is commutative.
What is commutative ring in Tamil?
Commutative ring in Tamil is பரிமாற்று வளையம். See Commutative ring meaning in Tamil.
How do you use commutative ring in a sentence?
As usual, it is simpler to begin by looking at a more general setting—in this case, commutative rings—before getting involved with polynomial rings.
What part of speech is commutative ring?
Commutative ring is a noun.
What is the plural of commutative ring?
The plural of commutative ring is commutative rings.

Words near commutative ring in the dictionary

  1. commutative algebras
  2. commutative group
  3. commutative groups
  4. commutative justice
  5. commutative justices
  6. commutative ring
  7. commutative rings
  8. commutatively
  9. commutativeness
  10. commutativities
  11. commutativity

Source and license

Adapted from Wiktionary: commutative ring (page history and authors); commutative ring (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “commutative ring.” Word.ws, https://word.ws/commutative_ring. Based on Wiktionary, CC BY-SA 4.0.