理想数据库
Ideal Databases
摘要：
从代数几何的角度来看，数据库关系被简洁地定义为有限簇。在建立基本框架后，从数据库依赖性理论出发，给出了Heath定理的解析证明。接下来，我们利用代数/几何字典，专注于有限簇的代数对应物，多项式理想。理想的交与和都是格运算.我们将这一事实推广到不同环的理想，从而建立理想代数是关系格。最后一站是将框架铸造成线性代数，并穿越到量子理论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
