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| 1 | Field |
| 1 | Converse Theorem |
| 1 | Implication |
| 1 | Ring |
| 1 | Subring |
| 3 | Finite Extension |
| 4 | Finitely Generated R Module |
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Module Finite
We say that 
is module-finite over 
if 
is finitely generated
as an 
-module.
We say that 
is ring-finite over 
if
![$ S=R[v_1,\ldots,v_n]$](http://myyn.org/static/assets/mathbrowser/article/5997/images/img9.png){kind=small}
for some
.
Note that module-finite implies ring-finite, but the converse is false.
If 
is ring-finite over 
, with 
fields, then 
is a finite extension
of 
.