Itthenfollows that if is a graded ring over a local ring, is a homomorphic image of a polynomial ring over a regular local ring. For the sake of brevity, we refer to a graded polynomial ring over a regular local ring simply as a graded polynomial ring.
2000, Paul M. Cohn, Introduction to Ring Theory, Springer, page 106,
If is any right Noetherian ring, the polynomial ring is again right Noetherian.
2009, Jesse Elliott, Some new approaches to integer-valued polynomial rings, Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson (editors), Commutative Algebra and Its Applications: Proceedings of the 5th International Fez Conference, Walter de Gruyter, page 223,
is called the polynomial ring (または ring of polynomials) inover.
The notation is standardly used for the case of a polynomial ring in multiple variables.
It is possible to speak of a polynomial ring in an infinite set of variables, provided it is assumed that any individual polynomial depends only on a finite number of variables.
同意語
(ring formed from polynomials):polynomial algebra, ring of polynomials