NULLSTELLENSATZ FOR RELATIVE EXISTENTIALLY CLOSED GROUPS

Mohammad Shahryari

doi:10.22108/ijgt.2021.125453.1652

NULLSTELLENSATZ FOR RELATIVE EXISTENTIALLY CLOSED GROUPS

Mohammad Shahryari^*

^*Corresponding author for this work

Mathematics

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

1 Citation (Scopus)

Abstract

We prove that in every variety of G-groups, every G-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize Theorem G of [J. Algebra, 219 (1999) 16–79]. As a result we see that every pair of G-existentially closed elements in an arbitrary variety of G-groups generate the same quasi-variety and if both of them are q_ω-compact, they are geometrically equivalent.

Original language	English
Pages (from-to)	125-130
Number of pages	6
Journal	International Journal of Group Theory
Volume	11
Issue number	2
DOIs	https://doi.org/10.22108/ijgt.2021.125453.1652
Publication status	Published - Jun 2022

Keywords

Algebraic geometry over groups
Existentially closed groups
Nullstellensatz
Quasi-varieties
Varieties of groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.22108/ijgt.2021.125453.1652

Cite this

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title = "NULLSTELLENSATZ FOR RELATIVE EXISTENTIALLY CLOSED GROUPS",

abstract = "We prove that in every variety of G-groups, every G-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize Theorem G of [J. Algebra, 219 (1999) 16–79]. As a result we see that every pair of G-existentially closed elements in an arbitrary variety of G-groups generate the same quasi-variety and if both of them are qω-compact, they are geometrically equivalent.",

keywords = "Algebraic geometry over groups, Existentially closed groups, Nullstellensatz, Quasi-varieties, Varieties of groups",

author = "Mohammad Shahryari",

note = "Publisher Copyright: {\textcopyright} 2021 University of Isfahan.",

year = "2022",

month = jun,

doi = "10.22108/ijgt.2021.125453.1652",

language = "English",

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AB - We prove that in every variety of G-groups, every G-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize Theorem G of [J. Algebra, 219 (1999) 16–79]. As a result we see that every pair of G-existentially closed elements in an arbitrary variety of G-groups generate the same quasi-variety and if both of them are qω-compact, they are geometrically equivalent.

KW - Algebraic geometry over groups

KW - Existentially closed groups

KW - Nullstellensatz

KW - Quasi-varieties

KW - Varieties of groups

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JO - International Journal of Group Theory

JF - International Journal of Group Theory

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ER -

NULLSTELLENSATZ FOR RELATIVE EXISTENTIALLY CLOSED GROUPS

Abstract

Keywords

ASJC Scopus subject areas

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