On the irreducibility of a class of polynomials, III

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8 Citations (Scopus)

Abstract

This work is a continuation and extension of our earlier articles on irreducible polynomials. We investigate the irreducibility of polynomials of the form g(f(x)) over an arbitrary but fixed totally real algebraic number field L, where g(x) and f(x) are monic polynomials with integer coefficients in L, g is irreducible over L and its splitting field is a totally imaginary quadratic extension of a totally real number field. A consequence of our main result is as follows. If g is fixed then, apart from certain exceptions f of bounded degree, g(f(x)) is irreducible over L for all f having distinct roots in a given totally real number field.

Original languageEnglish
Pages (from-to)164-181
Number of pages18
JournalJournal of Number Theory
Volume15
Issue number2
DOIs
Publication statusPublished - 1982

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Irreducibility
Number field
Splitting Field
Irreducible polynomial
Algebraic number Field
Monic polynomial
Polynomial
Exception
Continuation
Roots
Distinct
Integer
Arbitrary
Coefficient
Class
Form

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the irreducibility of a class of polynomials, III. / Györy, K.

In: Journal of Number Theory, Vol. 15, No. 2, 1982, p. 164-181.

Research output: Contribution to journalArticle

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