双循环半群的ω扩张

数学季刊 ›› 2009, Vol. 24 ›› Issue (3): 415-419.

双循环半群的ω扩张

School of Mathematics and Computer Engineering, Xihua University

收稿日期:2007-10-09 出版日期:2009-09-30 发布日期:2023-06-29
作者简介: ZHU Wen(1964-), female, native of Nanjing, Jiangsu, an associate professor of Xihua University, engages in semigroup.
基金资助:
Supported by the NNSF of China(60473030； 60773035)；

ω-Extension of Bicyclic Semigroup

School of Mathematics and Computer Engineering, Xihua University

Received:2007-10-09 Online:2009-09-30 Published:2023-06-29
About author: ZHU Wen(1964-), female, native of Nanjing, Jiangsu, an associate professor of Xihua University, engages in semigroup.
Supported by:
Supported by the NNSF of China(60473030； 60773035)；

摘要/Abstract

摘要： In this paper, we discussed ω-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.

关键词: bicyclic semigroup, strong semilatlice, group congruence, pure idempotent
congruence

Abstract: In this paper, we discussed ω-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.

Key words: bicyclic semigroup, strong semilatlice, group congruence, pure idempotent
congruence

中图分类号:

O152.7

朱雯, 詹亮 . 双循环半群的ω扩张[J]. 数学季刊, 2009, 24(3): 415-419.

ZHU Wen, ZHAN Liang. ω-Extension of Bicyclic Semigroup[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 415-419.

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