On parameterized differential Galois extensions

Omar Sanchez; Joel Nagloo

doi:10.1016/j.jpaa.2015.12.001

On parameterized differential Galois extensions

Omar Sanchez, Joel Nagloo

City University of New York

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

160 Downloads (Pure)

Abstract

We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in Wibmer (2012) [16]. We also consider an extension of the results in Kamensky and Pillay (2014) [4] from the ODE case to the parameterized PDE case. More precisely, we show that if DD and Δ are two distinguished sets of derivations and (KD,Δ)(KD,Δ) is existentially closed in (K,Δ)(K,Δ), where K is a D∪ΔD∪Δ-field of characteristic zero, then every (parameterized) logarithmic equation over K has a parameterized strongly normal extension.

Original language	English
Pages (from-to)	2549-2563
Journal	Journal of Pure and Applied Algebra
Volume	220
Issue number	7
Early online date	6 Jan 2016
DOIs	https://doi.org/10.1016/j.jpaa.2015.12.001
Publication status	Published - Jul 2016

Access to Document

10.1016/j.jpaa.2015.12.001

QE_PV

Cite this

@article{36855092404646feb5602181c1bfe016,

title = "On parameterized differential Galois extensions",

abstract = "We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in Wibmer (2012) [16]. We also consider an extension of the results in Kamensky and Pillay (2014) [4] from the ODE case to the parameterized PDE case. More precisely, we show that if DD and Δ are two distinguished sets of derivations and (KD,Δ)(KD,Δ) is existentially closed in (K,Δ)(K,Δ), where K is a D∪ΔD∪Δ-field of characteristic zero, then every (parameterized) logarithmic equation over K has a parameterized strongly normal extension.",

author = "Omar Sanchez and Joel Nagloo",

year = "2016",

month = jul,

doi = "10.1016/j.jpaa.2015.12.001",

language = "English",

volume = "220",

pages = "2549--2563",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier BV",

number = "7",

}

TY - JOUR

T1 - On parameterized differential Galois extensions

AU - Sanchez, Omar

AU - Nagloo, Joel

PY - 2016/7

Y1 - 2016/7

N2 - We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in Wibmer (2012) [16]. We also consider an extension of the results in Kamensky and Pillay (2014) [4] from the ODE case to the parameterized PDE case. More precisely, we show that if DD and Δ are two distinguished sets of derivations and (KD,Δ)(KD,Δ) is existentially closed in (K,Δ)(K,Δ), where K is a D∪ΔD∪Δ-field of characteristic zero, then every (parameterized) logarithmic equation over K has a parameterized strongly normal extension.

AB - We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in Wibmer (2012) [16]. We also consider an extension of the results in Kamensky and Pillay (2014) [4] from the ODE case to the parameterized PDE case. More precisely, we show that if DD and Δ are two distinguished sets of derivations and (KD,Δ)(KD,Δ) is existentially closed in (K,Δ)(K,Δ), where K is a D∪ΔD∪Δ-field of characteristic zero, then every (parameterized) logarithmic equation over K has a parameterized strongly normal extension.

U2 - 10.1016/j.jpaa.2015.12.001

DO - 10.1016/j.jpaa.2015.12.001

M3 - Article

SN - 0022-4049

VL - 220

SP - 2549

EP - 2563

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

ER -

On parameterized differential Galois extensions

Abstract

Access to Document

Fingerprint

Cite this