Journal article
Nilpotent ideals in polynomial and power series rings
Proceedings of the American Mathematical Society, Vol.138(5), pp.1607-1619
05/01/2010
DOI: 10.1090/S0002-9939-10-10252-4
Abstract
Given a ring R and polynomials f(x),g(x) ∈ R[x] satisfying f (x)Rg(x) = 0, we prove that the ideal generated by products of the coefficients of f (x)and g(x) is nilpotent. This result is generalized, and many well known facts, along with new ones, concerning nilpotent polynomials and power series are obtained. We also classify which of the standard nilpotence properties on ideals pass to polynomial rings or from ideals in polynomial rings to ideals of coefficients in base rings. In particular, we prove that if I ≤ R[x]is aleft T-nilpotent ideal, then the ideal formed by the coefficients of polynomials in I is also left T-nilpotent.
Details
- Title: Subtitle
- Nilpotent ideals in polynomial and power series rings
- Creators
- Victor Camillo - University of Iowa, MathematicsChan Yong Hong - Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 131-701, Republic of KoreaNam Kyun Kim - Hanbat National UniversityYang Lee - Pusan National UniversityPace P. Nielsen - Brigham Young University
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.138(5), pp.1607-1619
- DOI
- 10.1090/S0002-9939-10-10252-4
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 13
- Language
- English
- Date published
- 05/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9983985803202771
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