论文标题
半群和相关结构的有限覆盖物
Finite Coverings of Semigroups and Related Structures
论文作者
论文摘要
对于Semigroup $ s $，相对于Semigroups的$ S $的覆盖率，$σ_s（s）$，是$ s $的最低适当子群的数量，其$ s $是$ s $。本文研究了涵盖半群的数量，并类似地定义了覆盖数量的反向半群和单型。我们的三个主要定理对有限的半群，有限的逆半群和单型（Modulo组和无限半群）提供了完整的描述。对于既不是单基因也不是群体的有限半群，其覆盖率为两个。对于所有$ n \ geq 2 $，存在一个反向半群，覆盖数$ n $，类似于循环。最后，一个既不是一个群体也不是具有身份的半群的单型物体也覆盖了第二名。
For a semigroup $S$, the covering number of $S$ with respect to semigroups, $σ_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$. This article investigates covering numbers of semigroups and analogously defined covering numbers of inverse semigroups and monoids. Our three main theorems give a complete description of the covering number of finite semigroups, finite inverse semigroups, and monoids (modulo groups and infinite semigroups). For a finite semigroup that is neither monogenic nor a group, its covering number is two. For all $n\geq 2$, there exists an inverse semigroup with covering number $n$, similar to the case of loops. Finally, a monoid that is neither a group nor a semigroup with an identity adjoined has covering number two as well.
