Ideal Databases
V Tropashko - arXiv preprint arXiv:1601.00524, 2015 - arxiv.org
V Tropashko
arXiv preprint arXiv:1601.00524, 2015•arxiv.orgFrom 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 …
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 …
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.
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