### 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 language | English |
---|---|

Pages (from-to) | 164-181 |

Number of pages | 18 |

Journal | Journal of Number Theory |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

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

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 15, no. 2, pp. 164-181. https://doi.org/10.1016/0022-314X(82)90023-3

}

TY - JOUR

T1 - On the irreducibility of a class of polynomials, III

AU - Györy, K.

PY - 1982

Y1 - 1982

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33748575555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748575555&partnerID=8YFLogxK

U2 - 10.1016/0022-314X(82)90023-3

DO - 10.1016/0022-314X(82)90023-3

M3 - Article

AN - SCOPUS:33748575555

VL - 15

SP - 164

EP - 181

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -