Back to Search
Start Over
Annihilating properties of ideals generated by coefficients of polynomials and power series.
- Source :
-
International Journal of Algebra & Computation . Mar2022, Vol. 32 Issue 2, p237-249. 13p. - Publication Year :
- 2022
-
Abstract
- In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if f (x) R g (x) = 0 for polynomials f (x) = ∑ i = 0 m a i x i , g (x) = ∑ j = 0 m b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i 1 R a i 2 R ⋯ a i s (i , j) R b j = 0 and a i R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 , whenever i 1 , i 2 , ... , i s (i , j) ≤ i and j 1 , j 2 , ... , j t (i , j) ≤ j. Next we prove that if f (x) R g (x) = 0 for power series f (x) = ∑ i = 0 ∞ a i x i , g (x) = ∑ j = 0 ∞ b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i s (i , j) R ⋯ R a i 2 R a i 1 R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 when ∑ p = 1 s (i , j) i p + ∑ q = 1 t (i , j) j q < (s (i , j) + 1) (t (i , j) + 1) (i + 1) (j + 1) and i p ≤ i , j q ≤ j for each p , q. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POWER series
*POLYNOMIALS
*IDEALS (Algebra)
*POLYNOMIAL rings
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 32
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 155781877
- Full Text :
- https://doi.org/10.1142/S0218196722500114