论文标题
以禁忌亚结构定理为特征的各种懒惰岩浆
Varieties of Lazy Magmas Characterized by Forbidden Substructure Theorems
论文作者
论文摘要
岩浆（或Groupoid）是带有二进制操作$（a，f）$的集合。粗略地说，如果诸如$ f（x，f（f（y，z），u））$之类的构图依赖于最多两个变量，则据说岩浆很懒惰。最近，Kaprinai，Machida和Waldhauser描述了各种懒惰类固醇的晶格。 禁止的结构定理是一种在较大的$ b $内部的较小级$ a $作为$ b $中的所有元素，以避免某些子结构。例如，当它是晶格（较大的$ b $）并避免五角大楼和钻石时，晶格是分布式的（较小的$ a $）。 在本文中，我们通过禁止的子结构定理提供了所有对所有对懒惰的群体品种$ a \ le b $的表征。一些结果很简单，但另一些结果非常参与。所有这些结果和证明都是使用一种计算工具（对于许多不同类别的关系代数）的计算工具，并为每个数学家提供了。
A magma (or groupoid) is a set with a binary operation $(A,f)$. Roughly speaking, a magma is said to be lazy if compositions such as $f(x,f(f(y,z),u))$ depend on at most two variables. Recently, Kaprinai, Machida and Waldhauser described the lattice of all the varieties of lazy groupoids. A forbidden structure theorem is one that charcaterizes a smaller class $A$ inside a larger class $B$ as all the elements in $B$ that avoid some substructures. For example, a lattice is distributive (smaller class $A$) if and only if it is a lattice (larger class $B$) and avoids the pentagon and the diamond. In this paper we provide a characterization of all pairs of lazy groupoid varieties $A\le B$ by forbidden substructure theorems. Some of the results are straightforward, but some other are very involved. All of these results and proofs were found using a computational tool that proves theorems of this type (for many different classes of relational algebras) and that we make available to every mathematician.
