On Large Subsemigroups and Finiteness Conditions of Semigroups
On Large Subsemigroups and Finiteness Conditions of Semigroups
复制标题
关于大子半群和半群的有限条件
DOI：
10.1112/s0024611598000124
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发表时间：
1998
影响因子：
1.8
通讯作者：
N. Ruškuc
中科院分区：
文献类型：
--
作者：
N. Ruškuc
设是一个半群，设是的一个子半群。我们说，如果集合是有限的。或者，我们说这是一个。这是一个集合的基数，称为“的”，用[：]表示。本文研究了一个半群与一个大子半群的相似程度。因此，例如，它是有限的，当且仅当是有限的，这是一个不言自明的事实。稍微不那么平凡的是，我们有下面的定理。
Let be a semigroup and let be a subsemigroup of . We say that is if the set is finite. Alternatively, we say that is a of . The cardinality of the set is called the of in , and is denoted by [ : ]. In this paper we investigate how similar a semigroup and a large subsemigroup of are. Thus, for example, it is a self-evident fact that is finite if and only if is finite. Slightly less trivially, we have the following theorem.