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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Factorization of monic polynomials


Authors: William J. Heinzer and David C. Lantz
Journal: Proc. Amer. Math. Soc. 131 (2003), 1049-1052
MSC (1991): Primary 13B25, 13G05, 13J15.
Published electronically: July 26, 2002
MathSciNet review: 1948094
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Abstract: We prove a uniqueness result about the factorization of a monic polynomial over a general commutative ring into comaximal factors. We apply this result to address several questions raised by Steve McAdam. These questions, inspired by Hensel's Lemma, concern properties of prime ideals and the factoring of monic polynomials modulo prime ideals.


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Additional Information

William J. Heinzer
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email: heinzer@math.purdue.edu

David C. Lantz
Affiliation: Department of Mathematics, Colgate University, Hamilton, New York 13346-1398
Email: dlantz@mail.colgate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06636-4
PII: S 0002-9939(02)06636-4
Keywords: Hensel's Lemma, monic polynomial, comaximal ideals, H-prime, integral upper
Received by editor(s): August 27, 2001
Received by editor(s) in revised form: November 5, 2001
Published electronically: July 26, 2002
Additional Notes: The second author is grateful for the hospitality and support of Purdue University while this work was done.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2002 American Mathematical Society