On Gorenstein Fiber Products and Applications

Saeed Nasseh; Ryo Takahashi; Keller VandeBogert

On Gorenstein Fiber Products and Applications

Saeed Nasseh, Ryo Takahashi, Keller VandeBogert

Mathematical Sciences

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Abstract

We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.

Original language	American English
Journal	arXIV.org Repository
State	Published - Jan 30 2017

Disciplines

Education
Mathematics

Keywords

Fiber applications
Fiber product
Gorenstein fiber products
Local rings

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On Gorenstein Fiber Products and ApplicationsFinal published version, 270 KBLicense: Unspecified

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title = "On Gorenstein Fiber Products and Applications",

abstract = " We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.",

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T1 - On Gorenstein Fiber Products and Applications

AU - Nasseh, Saeed

AU - Takahashi, Ryo

AU - VandeBogert, Keller

PY - 2017/1/30

Y1 - 2017/1/30

N2 - We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.

AB - We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.

KW - Fiber applications

KW - Fiber product

KW - Gorenstein fiber products

KW - Local rings

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/421

M3 - Article

JO - arXIV.org Repository

JF - arXIV.org Repository

ER -

On Gorenstein Fiber Products and Applications

Abstract

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Keywords

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