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How to pronounce “prime ideal”
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Pronunciation guide for prime ideal
- Learning goal
- Practice the English pronunciation of prime ideal with real speech in context.
- Available examples
- 0 YouTube examples
- Definition summary
- (algebra, ring theory) Any (two-sided) ideal
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A Deep Dive Into “prime ideal”
Meaning
- [Noun]
- (algebra, ring theory) Any (two-sided) ideal
- I
- {\displaystyle I}
- such that for arbitrary ideals
- P
- {\displaystyle P}
- and
- Q
- {\displaystyle Q}
- ,
- P
- Q
- ⊆
- I
- ⟹
- P
- ⊆
- I
- {\displaystyle PQ\subseteq I\implies P\subseteq I}
- or
- Q
- ⊆
- I
- {\displaystyle Q\subseteq I}
- .
- In a commutative ring, a (two-sided) ideal
- I
- {\displaystyle I}
- such that for arbitrary ring elements
- a
- {\displaystyle a}
- and
- b
- {\displaystyle b}
- ,
- a
- b
- ∈
- I
- ⟹
- a
- ∈
- I
- {\displaystyle ab\in I\implies a\in I}
- or
- b
- ∈
- I
- {\displaystyle b\in I}
- .
Practice Nearby Words
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Similar Sounds
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