Definition of prime ideal：Section 27
Section 27
Prime ideal
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In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the ...
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 ...
2
https://uomustansiriyah.edu.iq
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 ⇐ ...