理论数学  >> Vol. 7 No. 6 (November 2017)

关于完全π-正则半群类的禁止因子的注记
A Note on the Forbidden Epidivisors of Some Subclasses of Epigroups

DOI: 10.12677/PM.2017.76056, PDF, HTML, XML, 下载: 822  浏览: 1,054  科研立项经费支持

作者: 高 凯, 刘靖国*:临沂大学数学与统计学院,山东 临沂

关键词: 完全π-正则半群禁止因子等式类Epigroup Forbidden Epidivisor Equation

摘要: 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。论文在给出核为完全正则半群的完全π-正则半群类的刻画基础上,利用禁止因子和等式刻画了该型半群的推广类。同时讨论核为带的完全π-正则半群的特殊情形。
Abstract: A semigroup is called an epigroup if for each element in this given semigroup, some power of the element lies in some subgroup of the given semigroup. In this paper based on the given characterizations of epigroups in which the idempotent-generated subsemigroups are completely regular, we give some descriptions of some subclasses of epigroups in terms of identities, and forbidden epidivisors. For a special case, epigroups in which the kernels are bands are also characterized.

文章引用: 高凯, 刘靖国. 关于完全π-正则半群类的禁止因子的注记[J]. 理论数学, 2017, 7(6): 431-436. https://doi.org/10.12677/PM.2017.76056

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