Compactness Conditions in Universal Algebraic Geometry

P. Modabberi; M. Shahryari

doi:10.1007/s10469-016-9384-7

Compactness Conditions in Universal Algebraic Geometry

P. Modabberi^*, M. Shahryari

^*Corresponding author for this work

Mathematics

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

5 Citations (Scopus)

Abstract

Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, q_ω-compactness, and u_ω-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.

Original language	English
Pages (from-to)	146-172
Number of pages	27
Journal	Algebra and Logic
Volume	55
Issue number	2
DOIs	https://doi.org/10.1007/s10469-016-9384-7
Publication status	Published - May 1 2016

Keywords

Hilbert’s basis theorem
Zariski topology
algebraic sets
algebraic structures
coordinate algebra
equational domains
equationally Artinian algebras
equationally Noetherian algebras
equations
free algebras
metacompact algebras
metacompact spaces
prevarieties
q-compactness
radical ideal
u-compactness
varieties

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Logic

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10.1007/s10469-016-9384-7

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title = "Compactness Conditions in Universal Algebraic Geometry",

abstract = "Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, qω-compactness, and uω-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.",

keywords = "Hilbert{\textquoteright}s basis theorem, Zariski topology, algebraic sets, algebraic structures, coordinate algebra, equational domains, equationally Artinian algebras, equationally Noetherian algebras, equations, free algebras, metacompact algebras, metacompact spaces, prevarieties, q-compactness, radical ideal, u-compactness, varieties",

author = "P. Modabberi and M. Shahryari",

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year = "2016",

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AU - Modabberi, P.

AU - Shahryari, M.

PY - 2016/5/1

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N2 - Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, qω-compactness, and uω-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.

AB - Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, qω-compactness, and uω-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.

KW - Hilbert’s basis theorem

KW - Zariski topology

KW - algebraic sets

KW - algebraic structures

KW - coordinate algebra

KW - equational domains

KW - equationally Artinian algebras

KW - equationally Noetherian algebras

KW - equations

KW - free algebras

KW - metacompact algebras

KW - metacompact spaces

KW - prevarieties

KW - q-compactness

KW - radical ideal

KW - u-compactness

KW - varieties

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JO - Algebra and Logic

JF - Algebra and Logic

IS - 2

ER -

Compactness Conditions in Universal Algebraic Geometry

Abstract

Keywords

ASJC Scopus subject areas

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