Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B25, 13G05, 13J15.

Retrieve articles in all journals with MSC (1991): 13B25, 13G05, 13J15.

Additional Information

William J. Heinzer
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

David C. Lantz
Affiliation: Department of Mathematics, Colgate University, Hamilton, New York 13346-1398

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

American Mathematical Society