Going up

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Last seen on: –LA Times Crossword 16 Jan 21, Saturday
Irish Times Simplex – Nov 7 2020

Random information on the term “Going up”:

In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions.

The phrase going up refers to the case when a chain can be extended by “upward inclusion”, while going down refers to the case when a chain can be extended by “downward inclusion”.

The major results are the Cohen–Seidenberg theorems, which were proved by Irvin S. Cohen and Abraham Seidenberg. These are known as the going-up and going-down theorems.

Let A ⊆ B be an extension of commutative rings.

The going-up and going-down theorems give sufficient conditions for a chain of prime ideals in B, each member of which lies over members of a longer chain of prime ideals in A, to be able to be extended to the length of the chain of prime ideals in A.

First, we fix some terminology. If p {\displaystyle {\mathfrak {p}}} and q {\displaystyle {\mathfrak {q}}} are prime ideals of A and B, respectively, such that

Going up on Wikipedia