Factorial fermat curves over the rational numbers

Peter Malcolmson; Frank Okoh; Vasuvedan Srinivas

doi:10.4064/cm142-2-9

Factorial fermat curves over the rational numbers

Peter Malcolmson
, Frank Okoh
, Vasuvedan Srinivas

Mathematics

Wayne State University

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

1 Scopus citations

Abstract

A polynomial f in the set {X ⁿ + Y ⁿ , X ⁿ + Y ⁿ − Z ⁿ , X ⁿ + Y ⁿ + Z ⁿ , X ⁿ +Y ⁿ −1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.

Original language	English
Pages (from-to)	285-300
Number of pages	16
Journal	Colloquium Mathematicum
Volume	142
Issue number	2
DOIs	https://doi.org/10.4064/cm142-2-9
State	Published - 2016

Keywords

Coordinate rings
Factorial
Half-factorial

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10.4064/cm142-2-9

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abstract = "A polynomial f in the set \{X n + Y n , X n + Y n − Z n , X n + Y n + Z n , X n +Y n −1\} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.",

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AU - Okoh, Frank

AU - Srinivas, Vasuvedan

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2016.

PY - 2016

Y1 - 2016

N2 - A polynomial f in the set {X n + Y n , X n + Y n − Z n , X n + Y n + Z n , X n +Y n −1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.

AB - A polynomial f in the set {X n + Y n , X n + Y n − Z n , X n + Y n + Z n , X n +Y n −1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.

KW - Coordinate rings

KW - Factorial

KW - Half-factorial

UR - https://www.scopus.com/pages/publications/84956931098

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DO - 10.4064/cm142-2-9

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JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

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ER -

Factorial fermat curves over the rational numbers

Abstract

Keywords

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