prime ideal
A "prime ideal" is a fundamental concept in ring theory, analogous to prime numbers in integer arithmetic, and has significant applications in algebraic geometry and number theory.
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Definition
C2Ring Theory
(technical, academic)A subset of a ring such that if the product of any two elements of the ring is in this subset, then at least one of those elements is also in the subset.
Example
- In the ring of integers, the set of multiples of a prime number forms a prime ideal.
- Prime ideals are crucial in defining the spectrum of a ring, a key concept in algebraic geometry.
Similar
Terms that have similar or relatively close meanings to "prime ideal":
prime numberalmost primeprime factorprimitive elementprincipal ideal ringrelatively primeprime number theoremassociated primeprimitive polynomialprime ring