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An algorithm for the divisors of monic polynomials over a commutative ring

✍ Scribed by Ihsen Yengui

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 147 KB
Volume: 260
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310108

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✦ Synopsis

Gilmer and Heinzer proved that given a reduced ring R, a polynomial f divides a monic polynomial in R[X] if and only if there exists a direct sum decomposition of R = R0 ⊕ . . . ⊕ Rm (m ≤ deg f ), associated to a fundamental system of idempotents e0, . . . , em, such that the component of f in each Ri[X] has degree coefficient which is a unit of Ri. We propose to give an algorithm to explicitly find such a decomposition. Moreover, we extend this result to divisors of doubly monic Laurent polynomials.

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