| 摘要: |
| 一个半群是Clifford半群当且仅当它是群的强半格，π-群是群在π-正则半群范围内的推广.同余是研究半群性质和结构的重要手段和工具.研究了π-群的强半格上的正则同余，并给出了π-群强半格上的同余是正则同余的充要条件. |
| 关键词: π-群 强半格 正则同余 正规子群 |
| DOI：10.3969/J.ISSN.1000-5137.2022.03.008 |
| 分类号:O152.7 |
| 基金项目:国家自然科学基金(11671056) |
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| Congruence on a strong semilattice of π-groups |
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DAI Luyao1, ZHANG Jiangang2, SHEN Ran3
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1.Shanghai Jiangning School, Shanghai 200060, China;2.Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China;3.College of Science, Donghua University, Shanghai 201620, China
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| Abstract: |
| It is well known that a semigroup is a Clifford semigroup， if and only if it is a strong semilattice of groups， and the class of π-groups is the generalization of groups in the range of π-regular semigroups. Congruence is an important tool when studying the characterization and structure of a semigroup. In this paper， we consider the regular congruences on a strong semilattice of π-groups， and give necessary and sufficient conditions for a congruence on a strong semilattice of π-groups to be a regular congruence. |
| Key words: π-groups strong semilattice regular congruence normal subgroup |
