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Dividing polynomials using the resultant matrix

Title
Dividing polynomials using the resultant matrix
Authors
Woo S.S.
Ewha Authors
우성식
SCOPUS Author ID
우성식scopus
Issue Date
2007
Journal Title
Communications in Algebra
ISSN
0092-7872JCR Link
Citation
vol. 35, no. 11, pp. 3263 - 3272
Indexed
SCIE; SCOPUS WOS scopus
Abstract
Let f, g be polynomials over a Noetherian ring A. We use the matrix coming from the resultant of f and g to get a criterion for divisibility of f by g in terms of Fitting invariants as well as a method of dividing polynomials once we know g divides f. Further we show that this is equivalent to that cokernel or the image of the multiplication-by-g map on A[X]/(f) is free. As an application we show one can test irreducibility of an integral polynomial by computing minors of a matrix.
DOI
10.1080/00927870701658185
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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