Definition of prime ideal：Prime ideal
Prime ideal
Inalgebra,aprimeidealisasubsetofaringthatsharesmanyimportantpropertiesofaprimenumberintheringofintegers.Theprimeidealsforthe ...。其他文章還包含有：「PrimeIdeal」、「Whatisaprimeideal?」、「3.Primeandmaximalideals3.1.DefinitionsandExamples...」、「8.4」、「Primeideals:definition」、「primeidealinnLab」、「Section27」、「2」、「1.2.primeideals.」
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Prime Ideal
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A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (ie, the multiples of p) is prime.
What is a prime ideal?
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What is a prime ideal? · If a and b are two elements of R such that their product ab is an element of P, then a is in P or b is in P, · P is not ...
3. Prime and maximal ideals 3.1. Definitions and Examples ...
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Definitions and Examples. Definition. An ideal P in a ring A is called prime if P 6= A and if for every pair x, y of elements in A-P we have xy 6∈ P. ...
8.4
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An ideal P is called a prime ideal if P≠R and whenever the product ab∈P for a,b∈R, then at least one of a or b is in P. Example 8.4.3. In any ...
Prime ideals: definition
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In Z, the prime ideals correspond to the principal ideal (p) generated by prime numbers. Every non-zero prime ideal in Z is also maximal.
prime ideal in nLab
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Prime ideals are supposed to be a generalization of prime numbers from elements of the ring of integers to ideals in the sense of 'ideal elements' of an ...
Section 27
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Prime ideals. Definition (27.13) An ideal P 6= R in a commutative ring is a prime ideal if ab ∈ P implies a ∈ P or b ∈ P. Example. 1.
2
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An ideal (I,+, . ) of the ring (R , + , . )is called Prime ideal if such that I , then either I or I . Example (1): In a ring ( , , ) an ideal ...
1.2. prime ideals.
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Definition 1.12. A prime ideal is a proper ideal whose complement is closed under multiplication. This is equivalent to saying: ab ∈ p ⇐ ...