Nilpotent ideals in polynomial and power series rings
Authors:
Victor Camillo, Chan Yong Hong, Nam Kyun Kim, Yang Lee and Pace P. Nielsen
Journal:
Proc. Amer. Math. Soc. 138 (2010), 16071619
MSC (2000):
Primary 16N40; Secondary 16U80
Published electronically:
January 13, 2010
MathSciNet review:
2587445
Fulltext PDF
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Abstract: Given a ring and polynomials satisfying , we prove that the ideal generated by products of the coefficients of and 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 is a left nilpotent ideal, then the ideal formed by the coefficients of polynomials in is also left nilpotent.
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Additional Information
Victor Camillo
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
camillo@math.uiowa.edu
Chan Yong Hong
Affiliation:
Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 131701, Republic of Korea
Email:
hcy@khu.ac.kr
Nam Kyun Kim
Affiliation:
College of Liberal Arts, Hanbat National University, Daejon 305719, Republic of Korea
Email:
nkkim@hanbat.ac.kr
Yang Lee
Affiliation:
Department of Mathematics Education, Pusan National University, Pusan 609735, Republic of Korea
Email:
ylee@pusan.ac.kr
Pace P. Nielsen
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
pace@math.byu.edu
DOI:
http://dx.doi.org/10.1090/S0002993910102524
Keywords:
Bounded index of nilpotence,
left $T$nilpotent,
locally nilpotent,
nil,
nilpotent,
polynomial ring,
power series ring
Received by editor(s):
June 9, 2009
Received by editor(s) in revised form:
September 15, 2009
Published electronically:
January 13, 2010
Communicated by:
Birge HuisgenZimmermann
Article copyright:
© Copyright 2010
By the authors
