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Computer Science > Databases

arXiv:1601.00524 (cs)
[Submitted on 30 Dec 2015 (v1), last revised 12 Dec 2017 (this version, v2)]

Title:Ideal Databases

Authors:Vadim Tropashko
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Abstract:From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage Algebra/Geometry dictionary and focus on algebraic counterparts of finite varieties, polynomial ideals. It is well known that intersection and sum of ideals are lattice operations. We generalize this fact to ideals from different rings, therefore establishing that algebra of ideals is Relational Lattice. The final stop is casting the framework into Linear Algebra, and traversing to Quantum Theory.
Comments: Amended the introduction; added CoCoA section
Subjects: Databases (cs.DB)
Cite as: arXiv:1601.00524 [cs.DB]
  (or arXiv:1601.00524v2 [cs.DB] for this version)
  https://doi.org/10.48550/arXiv.1601.00524

Submission history

From: Vadim Tropashko [view email]
[v1] Wed, 30 Dec 2015 22:45:56 UTC (146 KB)
[v2] Tue, 12 Dec 2017 18:24:33 UTC (171 KB)
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