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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Distinct degree factorizations for polynomials over a finite field
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by Arnold Knopfmacher and Richard Warlimont PDF
Trans. Amer. Math. Soc. 347 (1995), 2235-2243 Request permission

Abstract:

Let ${\widetilde {\mathbb {F}}_q}[X]$ denote the multiplicative semigroup of monic polynomials in one indeterminate $X$, over a finite field ${\mathbb {F}_q}$. We determine for each fixed $q$ and fixed $n$ the probability that a polynomial of degree $n$ in ${\mathbb {F}_q}[X]$ has irreducible factors of distinct degrees only. These results are of relevance to various polynomial factorization algorithms.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2235-2243
  • MSC: Primary 11T06; Secondary 11T55
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1277121-X
  • MathSciNet review: 1277121