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.
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Translated from Algebra i Logika, Vol. 55, No. 2, pp. 219-256, March-April, 2016.
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Modabberi, P., Shahryari, M. Compactness Conditions in Universal Algebraic Geometry. Algebra Logic 55, 146–172 (2016). https://doi.org/10.1007/s10469-016-9384-7
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DOI: https://doi.org/10.1007/s10469-016-9384-7
Keywords
- algebraic structures
- equations
- algebraic sets
- radical ideal
- coordinate algebra
- Zariski topology
- equationally Noetherian algebras
- qω -compactness
- uω -compactness
- metacompact algebras
- metacompact spaces
- equationally Artinian algebras
- prevarieties
- varieties
- free algebras
- equational domains
- Hilbert’s basis theorem