论文标题
区块和大厅关系
Block-groups and Hall relations
论文作者
论文摘要
如果有限集中的二进制关系包含该集合的排列，则称为大厅关系。在通常的关系产品下，Hall关系形成了一个众所周知的块组，即，在每个$ \ mathrsfs {r} $ - 类和每个$ \ mathrsfs {l} $ class中，最多有一个具有一个diadempotent的半群。在这里，我们表明，从某种意义上说，相反的是真实的：每个区块组都在有限的集合上划分了霍尔关系的半群岛。
A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most one idempotent in each $\mathrsfs{R}$-class and each $\mathrsfs{L}$-class. Here we show that in a certain sense, the converse is true: every block-group divides a semigroup of Hall relations on a finite set.
