关于完全π-正则半群分块定义的一个注记
A Note on the Definitions of Blocks of Epigroups

DOI: 10.12677/PM.2016.62013, PP. 89-94

Keywords: 完全π-正则半群，分块，正则D-类
Epigroup, Block, Regular D-Class

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Abstract:

完全π-正则半群是其所含任意元的某个幂属于其最大子群的半群。论文给出了两个不同形式的半群分块的定义，证明当所给半群为完全π-正则半群时这两个定义是等价的。论文还提供了分块的第三个定义，证明当分块为子半群时，完全π-正则半群的第三个分块定义与前两者等价。
A semigroup is called an epigroup if for any element in this semigroup some power of the element lies in the maximal subgroup of the given semigroup. In this paper two variants of definitions of blocks of semigroups are given and we prove that two of them turn out to coincide in the case of epigroups. We also offer the third definition of blocks of epigroups and show that if blocks of epi-groups are subsemigroups, then this definition is equivalent to the other two.

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