simple ring
Word Rarity
Uncommon
Frequency: Zipf frequency 4.62 in modern English
15
Scrabble Score
10
Letters
2
Syllables
9
Unique Chars
Meaning
noun
A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).
Example Sentences
- "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."
- "By theorem 7.7.1 any field is a simple ring."
- "A field is clearly a simple ring. Indeed, a commutative simple ring with unity must be a field (Problem 1, Section 1). An example of a noncommutative simple ring is Fₙ, the n × n matrix ring over a field F, n > 1."
- "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. We shall see that every simple ring is isomorphic to M#95;n(D) for some n, and for some division ring D."
Inflected Forms
Phrases
semisimple ring
simple module
Frequently Paired Words
semisimple ring
simple module