On a theorem of Ore

Jesus Montes; Enric Nart

doi:10.1016/0021-8693(92)90071-S

On a theorem of Ore

Jesus Montes, Enric Nart

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

22 Citations (Scopus)

Abstract

O. Ore (Math. Ann. 99, 1928, 84-117) developed a method for obtaining the absolute discriminant and the prime-ideal decomposition of the rational primes in a number field K. The method, based on Newton's polygon techniques, worked only when certain polynomials f{hook}S(Y), attached to any side S of the polygon, had no multiple factors. These results are generalized in this paper finding a much weaker condition, effectively computable, under which it is still possible to give a complete answer to the above questions. The multiplicities of the irreducible factors of the polynomials f{hook}S(Y) play then an essential role. © 1992.

Original language	English
Pages (from-to)	318-334
Journal	Journal of Algebra
Volume	146
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(92)90071-S
Publication status	Published - 1 Jan 1992

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AB - O. Ore (Math. Ann. 99, 1928, 84-117) developed a method for obtaining the absolute discriminant and the prime-ideal decomposition of the rational primes in a number field K. The method, based on Newton's polygon techniques, worked only when certain polynomials f{hook}S(Y), attached to any side S of the polygon, had no multiple factors. These results are generalized in this paper finding a much weaker condition, effectively computable, under which it is still possible to give a complete answer to the above questions. The multiplicities of the irreducible factors of the polynomials f{hook}S(Y) play then an essential role. © 1992.

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