关系代数运算下的等价关系闭格
Lattices of Equivalence Relations Closed Under the Operations of Relation Algebras
摘要：
泛代数中一个长期存在的问题是有限格与有限代数的同余格同构的问题。这个问题可以表述为，哪些有限格可以表示为有限集上的等价关系在某些一阶公式下闭合的格。我们将这个问题推广到一阶公式的不同集合，并举例说明我们的新问题是不同的。然后，我们证明了每个格$\m M_n$可以表示在这种新的方式。[This是提交给\emph{Algebra Universalis}的论文的扩展版本。]
英文摘要：
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as lattices of equivalence relations on finite sets closed under certain first order formulas. We generalize this question to a different collection of first-order formulas, giving examples to demonstrate that our new question is distinct. We then prove that every lattice $\m M_n$ can be represented in this new way. [This is an extended version of a paper submitted to \emph{Algebra Universalis}.]
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。
