The possibility to allow an infinite set of indeterminates is not really a generalization, as the ordinary notion of polynomial ring allows for it.
32.
*PM : polynomial ring over integral domain, id = 6918-- WP guess : polynomial ring over integral domain-- Status:
33.
*PM : polynomial ring over integral domain, id = 6918-- WP guess : polynomial ring over integral domain-- Status:
34.
However, it is often easier to compute in the twisted polynomial ring this can be applied especially in the theory of Drinfeld modules.
35.
For example the implication labeled " local ring or PID " is also true for polynomial rings over a field : this is Quillen Suslin theorem.
36.
If is a subscheme of-dimensional projective space, then corresponds to a graded ideal of the polynomial ring in variables, with graded pieces.
37.
The generators of degrees 2, 4, 6, 10 generate a polynomial ring, which contains the square of the generator of degree 15.
38.
Formation of the polynomial ring, together with forming factor rings by factoring out ideals, are important tools for constructing new rings out of known ones.
39.
They are named for, who proved the unmixedness theorem for polynomial rings, and for, who proved the unmixedness theorem for formal power series rings.
40.
In general the Koszul complex is not an exact sequence, but " it is an exact sequence if one works with a polynomial ring"
