Examples of 'prime ideals' in a sentence
Meaning of "prime ideals"
prime ideals: In mathematics, specifically in the field of abstract algebra, prime ideals are special types of ideals within a ring that have properties similar to prime numbers in the context of integers. They play a significant role in the study of algebraic structures and have applications in various mathematical theories
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- plural of prime ideal
How to use "prime ideals" in a sentence
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prime ideals
Associated prime ideals and primary decomposition.
Let be the set of all prime ideals of.
Prime ideals for commutative rings.
Let be the set of prime ideals in containing.
It turns out that the irreducible varieties correspond to prime ideals.
The splitting of prime ideals in an extension field.
Such ideals are called prime ideals.
Let be the prime ideals containing.
Prime ideals can frequently be produced as maximal elements of certain collections of ideals.
It is the intersection of all prime ideals containing.
Prime ideals of R of length m.
The product of two prime ideals is their intersection.
Every nonzero ideal admits a unique factorization into a product of prime ideals.
The decomposition of prime ideals in extensions.
This follows from the fact that nilradical is the intersection of all prime ideals.
See also
Decomposition of prime ideals in finite extensions.
The Zariski topology defines a topology on the spectrum of a ring the set of prime ideals.
The sum of two prime ideals is not necessarily prime.
This fact is the ultimate generalization of the decomposition into prime ideals in Dedekind rings.
Factoring prime ideals in extensions.
Thus R contains finitely many minimal prime ideals.
Splitting of prime ideals in Galois extensions.
In fact, it is the intersection of all minimal prime ideals.
Splitting of prime ideals in a Galois extension.
Thus formula 5 is exactly the intersection of all prime ideals.
Completely prime ideals are prime ideals, but the converse is not true.
It then encodes the ramification data for prime ideals of the ring of integers.
In a commutative Noetherian ring, there are only finitely many minimal prime ideals.
Primitive ideals are prime, and prime ideals are both primary and semiprime.
The nilradical is equal to the intersection of all the ring 's prime ideals.
The non-closed points correspond to prime ideals which are not maximal.
For example, Krull defined the dimension of any commutative ring in terms of prime ideals.
Prime ideals for noncommutative rings [ edit ].
However, primary ideals which are associated with non-minimal prime ideals are in general not unique.
Hence, the nonzero prime ideals in Z are the ideals pZ, where p is.
In particular, the nilradical is the Jacobson radical since prime ideals are maximal.
Prime ideals and the spectrum = = = A particularly important type of ideals is " prime ideals ", often denoted " p.
See main article, Prime ideals.
Under this correspondence, ( equivalence classes ) of ultrametric places of F correspond to prime ideals of OF.
This makes the study of the prime ideals in " O " particularly important.
Any nonzero element of A { \ displaystyle A } is contained in only a finite number of height 1 prime ideals.
For f ∈ R, define Df to be the set of prime ideals of R not containing f.
Therefore, maximal ideals are G-ideals, and G-ideals are prime ideals.
The support of the module M is the set of prime ideals p such that Mp ≠ 0.
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