Structures · Algebra
Algebra.HasGoingUp
An R-algebra S satisfies Algebra.HasGoingUp R S if for every pair of
prime ideals p ≤ q of R with P a prime of S lying above p, there exists a
prime P ≤ Q of S lying above q.
The condition only asks for < which is easier to prove, use
Ideal.exists_ideal_ge_liesOver_of_le for applying it.
- Defined in
- Mathlib.RingTheory.Ideal.HasGoingUp
- Shape
- 2 explicit arguments · adds exists_ideal_ge_liesOver_of_lt
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