Factorization of monic polynomials

Heinzer, William; Lantz, David

doi:10.1090/S0002-9939-02-06636-4

Factorization of monic polynomials
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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