990个拟群等式定律的蕴含格
Implication semilattice of 990 quasigroup equational laws
AI总结：
本文研究990个拟群等式定律的蕴含关系，确定114个等价类及其中的蕴含结构，包含施罗德发现的非分配格。
摘要：
在试图反驳皮尔士关于所有格都是分配的断言时，恩斯特·施罗德135年前考虑了990个拟群等式定律，如$(x // y) * z = (y // x) \backslash\backslash z$。拟群是群的非结合类比，是配备乘法和右/左共轭除法运算的集合，这些运算相互兼容。每个等式将两个三变量表达式联系起来。本文确定了所有114个等价类的合取等价类，以及它们之间的蕴含关系。这包括施罗德发现的五元素非分配格作为其中的一个小角落。
英文摘要：
In his quest to disprove a claim by Peirce that all lattices are distributive, Ernst Schröder considered 135 years ago a list of 990 equational laws on quasigroups, analogous to associativity, such as $(x // y) * z = (y // x) \backslash\backslash z$. A quasigroup is a non-associative analogue of groups, specifically a set equipped with multiplication and right/left conjugate-division operations that are compatible. Each equation of interest identifies two three-variable expressions built from these operations. I determine all $114$ equivalence classes of their conjunctions, and all implications between them. This includes as a small corner the five-element non-distributive lattice identified by Schröder.
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。
