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Factorization of monic polynomials
Author(s):
William
J.
Heinzer;
David
C.
Lantz
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1049-1052.
MSC (1991):
Primary 13B25, 13G05, 13J15.
Posted:
July 26, 2002
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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.
References:
- 1.
- M. Artin, Algebra, Prentice Hall, Englewood Cliffs (1991). MR 92g:00001
- 2.
- W. Heinzer and S. Wiegand, Prime ideals in two-dimensional polynomial rings, Proc. Amer. Math. Soc. 107 (1989), 577-586. MR 90b:13010
- 3.
- E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser, Boston (1985). MR 86e:14001
- 4.
- S. McAdam, Strongly Comaximizable Primes, J. Algebra 170 (1994), 206-228. MR 95h:13008
- 5.
- S. McAdam, Unique factorization of monic polynomials, Comm. in Algebra 29 (2001), 4341-4343.
- 6.
- S. McAdam, Henselian-like prime ideas, Abstracts of Papers Presented to the American Mathematical Society 22(2) (2001), Abstract 964-13-51, 318.
- 7.
- M Nagata, Local Rings, Interscience, New York (1962). MR 27:5790; MR 57:301
- 8.
- D. Quillen, Projective modules over polynomial rings, Inv. Math. 36 (1976), 167-171. MR 55:337
- 9.
- A. Suslin, Projective modules over polynomial rings (Russian), Dokl. Akad. Nauk S.S.S.R. 26 (1978). MR 57:9685
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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:
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
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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