Word.ws English Dictionary

simple ring

simple ring noun: a ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).

Noun

simple ring (plural simple rings)

  1. (ring theory) A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).
    • Theorem 2. A semi-simple ring #92;mathfrak#123;A#125; satisfying the minimum condition can be decomposed in only one way as a direct sum of ideals which are simple rings.1956, Nathan Jacobson, Structure of Rings, American Mathematical Society, page 43
    • By theorem 7.7.1 any field is a simple ring.1969, Frederick Michael Hall, An Introduction to Abstract Algebra, volume 2, Cambridge University Press, page 195

simple ring meaning in Tamil

simple ring in Tamil

எளிய வளையம்

Examples of simple ring in a sentence

  • Indeed, a commutative simple ring with unity must be a field (Problem 1, Section 1).1994, P. B. Bhattacharya, S. K. Jain, S. R. Nagpaul, Basic Abstract Algebra, 2nd edition, Cambridge University Press, page 204:
  • Since M#95;n(D) has no nonzero proper two-sided ideals, it follows from the above discussion that M#95;n(D) is a left simple ring.2017, Ramji Lal, Algebra 2: Linear Algebra, Galois Theory, Representation theory, Group Extensions and Schur Multiplier, Springer, page 335:

Forms of simple ring

pluralsimple rings

Questions about simple ring

What does simple ring mean?
Simple ring means a ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).
What is simple ring in Tamil?
Simple ring in Tamil is எளிய வளையம். See Simple ring meaning in Tamil.
How do you use simple ring in a sentence?
Indeed, a commutative simple ring with unity must be a field (Problem 1, Section 1).
What part of speech is simple ring?
Simple ring is a noun.
What is the plural of simple ring?
The plural of simple ring is simple rings.

Words near simple ring in the dictionary

  1. simple pendulum
  2. simple pendulums
  3. simple present
  4. simple presents
  5. simple quadruple time
  6. simple ring
  7. simple rings
  8. simple root
  9. simple roots
  10. simple sentence
  11. simple sentences

Source and license

Adapted from Wiktionary: simple ring (page history and authors); simple 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: “simple ring.” Word.ws, https://word.ws/simple_ring. Based on Wiktionary, CC BY-SA 4.0.