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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-02-06636-4

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