论文标题
多态性同质量和通用代数几何形状
Polymorphism-homogeneity and universal algebraic geometry
论文作者
论文摘要
我们使用方程解决方程组以规范的方式为任何有限代数分配关系结构，我们证明这种关系结构是多态性的，并且仅当代数本身就是多态性的同性恋时。我们表明，多态性均匀性也等同于代数集（即方程式系统解决方案集）的属性，正是在代数的中央器克隆下封闭的一组。此外，我们证明，当代数在其有限的子能力类别中具有内向性时，上述属性就成立。我们还考虑了两个其他条件：多态性同质性和注射率的更强变体，我们明确描述了满足这三个条件中任何一个条件中任何一个条件中任何一种的有限半静止，格子，阿贝尔群和单位代数。
We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is polymorphism-homogeneous. We show that polymorphism-homogeneity is also equivalent to the property that algebraic sets (i.e., solution sets of systems of equations) are exactly those sets of tuples that are closed under the centralizer clone of the algebra. Furthermore, we prove that the aforementioned properties hold if and only if the algebra is injective in the category of its finite subpowers. We also consider two additional conditions: a stronger variant for polymorphism-homogeneity and for injectivity, and we describe explicitly the finite semilattices, lattices, Abelian groups and monounary algebras satisfying any one of these three conditions.
