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In mathematics, more specifically in ring theory, a maximal ideal is a two-sided ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other two-sided ideals contained between I and R.
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maximal ideal ring ideals right displaystyle prime rings two-sided simple left commutative module field mathbb set proper known generated quotient
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Maximal ideal | is a | two-sided ideal that is maximal | 0.90 | text |
| Maximal ideal | is a | prime ideal | 0.90 | text |
| Maximal ideal | related to Definition | There | 0.60 | section |
| Maximal ideal | related to Definition | Given | 0.60 | section |
| Maximal ideal | related to Definition | For | 0.60 | section |
| Maximal ideal | related to Definition | The | 0.60 | section |
| Maximal ideal | related to Definition | R/I | 0.60 | section |
| Maximal ideal | related to Examples | If | 0.60 | section |
| Maximal ideal | related to Examples | In | 0.60 | section |
| Maximal ideal | related to Examples | More | 0.60 | section |
| Maximal ideal | related to Examples | The | 0.60 | section |
| Maximal ideal | related to Examples | Generally | 0.60 | section |
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