polynomial ring उदाहरण वाक्य

उदाहरण वाक्य

1. Important examples are polynomial rings over the integers or over a field, Euclidean domains and principal ideal domains.
2. In his paper FAC, Serre asked whether a finitely generated projective module over a polynomial ring is free.
3. The concept and algorithms of Gr�bner bases have been generalized to submodules of free modules over a polynomial ring.
4. More generally, the Chevalley Shephard Todd theorem characterizes finite groups whose algebra of invariants is a polynomial ring.
5. A more general notion of polynomial ring is obtained when the distinction between these two formal products is maintained.
6. defined an analogous basis when the polynomial ring is replaced by the ring of exponentials of the weight lattice.
7. This case is closely related to work of Macaulay on graded polynomial rings and is sometimes called Macaulay duality.
8. For example, choosing a basis, a symmetric algebra satisfies the universal property and so is a polynomial ring.
9. Examples of Euclidean domains include fields, polynomial rings in one variable over a field, and the Gaussian integers.
10. This is equivalent to the statement that the polynomial ring is a free module over the ring of radical polynomials.