Going Up And Going Down
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 colloquially known as the going-up and going-down theorems.
Read more about Going Up And Going Down: Going Up and Going Down, Going-up and Going-down Theorems
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