Factorization of monic polynomials
HTML articles powered by AMS MathViewer
- by William J. Heinzer and David C. Lantz PDF
- Proc. Amer. Math. Soc. 131 (2003), 1049-1052 Request permission
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
- Michael Artin, Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991. MR 1129886
- William Heinzer and Sylvia Wiegand, Prime ideals in two-dimensional polynomial rings, Proc. Amer. Math. Soc. 107 (1989), no. 3, 577–586. MR 982402, DOI 10.1090/S0002-9939-1989-0982402-3
- Ernst Kunz, Introduction to commutative algebra and algebraic geometry, Birkhäuser Boston, Inc., Boston, MA, 1985. Translated from the German by Michael Ackerman; With a preface by David Mumford. MR 789602
- Stephen McAdam, Strongly comaximizable primes, J. Algebra 170 (1994), no. 1, 206–228. MR 1302838, DOI 10.1006/jabr.1994.1335
- S. McAdam, Unique factorization of monic polynomials, Comm. in Algebra 29 (2001), 4341–4343.
- S. McAdam, Henselian-like prime ideas, Abstracts of Papers Presented to the American Mathematical Society 22(2) (2001), Abstract 964-13-51, 318.
- H. Davenport and P. Erdös, On sums of positive integral $k$th powers, Ann. of Math. (2) 40 (1939), 553–536. MR 27, DOI 10.2307/1968937
- Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 427303, DOI 10.1007/BF01390008
- A. A. Suslin, Projective modules over polynomial rings are free, Dokl. Akad. Nauk SSSR 229 (1976), no. 5, 1063–1066 (Russian). MR 0469905
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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1049-1052
- MSC (1991): Primary 13B25, 13G05, 13J15
- DOI: https://doi.org/10.1090/S0002-9939-02-06636-4
- MathSciNet review: 1948094