Definition of prime ideal：8.4
8.4
2022年4月16日—AnidealPiscalledaprimeidealifP≠Randwhenevertheproductab∈Pfora,b∈R,thenatleastoneofaorbisinP.Example8.4.3.Inany ...。其他文章還包含有：「Primeideal」、「PrimeIdeal」、「Whatisaprimeideal?」、「3.Primeandmaximalideals3.1.DefinitionsandExamples...」、「Primeideals:definition」、「primeidealinnLab」、「Section27」、「2」、「1.2.primeideals.」
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Prime ideal
https://en.wikipedia.org
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
https://mathworld.wolfram.com
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?
https://math.stackexchange.com
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 ...
https://www.dpmms.cam.ac.uk
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. ...
Prime ideals: definition
https://math.stackexchange.com
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
https://ncatlab.org
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
https://jupiter.math.nycu.edu.
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
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.
https://people.brandeis.edu
Definition 1.12. A prime ideal is a proper ideal whose complement is closed under multiplication. This is equivalent to saying: ab ∈ p ⇐ ...