具有ωd, d′-型\mathcalD关系的正则单ω2-半群

商宇; 冯莹莹

doi:10.6054/j.jscnun.2024057

具有ω_{d, d′}-型 $\mathcal{D}$ 关系的正则单ω²-半群

商宇^1, ,,
冯莹莹²

1.
普洱学院数学与统计学院, 普洱 665000
2.
佛山科学技术学院数学与大数据学院, 佛山 528000

基金项目:

国家自然科学基金项目 11901088

普洱学院一流课程 2023YLKCZD010

详细信息

通讯作者:
商宇, Email: shangyu503@163.com

中图分类号: O152.7
计量
- 文章访问数: 29
- HTML全文浏览量: 10
- PDF下载量: 7
出版历程
- 收稿日期: 2024-01-06
- 刊出日期: 2024-08-24

Regular Simple ω²-Semigroups with ω_{d, d′}-Type $\mathcal{D}$ Relation

SHANG Yu^1, ,,
FENG Yingying²

1.
School of Mathematics and Statistics, Puer University, Puer 665000, China
2.
Department of Mathematics, Foshan University, Foshan 528000, China

摘要

摘要:
为得到正则单ω²-半群构造的刻画, 研究了具有ω_{d, d′}-型 $\mathcal{D}$ 关系的正则单ω²-半群: 从群的长度为(d, d′)的ω-链及其到群的同态出发, 借助Bruck-Reilly扩张, 获得了具有ω_{d, d′}-型 $\mathcal{D}$ 关系的正则单ω²-半群; 证明了任一个具有ω_{d, d′}-型 $\mathcal{D}$ 关系的正则单ω²-半群都可以用Bruck-Reilly扩张构造出来, 得到了这类半群的结构定理。
- 正则半群 /
- 单ω²-半群 /
- Bruck-Reilly扩张
Abstract:
To obtain the characterization of regular simple ω²-semigroups, the regular simple ω²-semigroups with ω_{d, d′}-type $\mathcal{D}$ relations are studied. Starting from the ω-chains of groups with length (d, d′) and the homomorphism from the ω-chains of groups with length (d, d′) to the group, by using Bruck-Reilly expansion, the regular simple ω²-semigroups with ω_{d, d′}-type $\mathcal{D}$ relations are obtained. It is proved that any regular simple ω²-semigroup with ω_{d, d′}-type $\mathcal{D}$ relations can be constructed by Bruck-Reilly extension, and the structure theorem of this kind of semigroups is obtained.
- regular semigroup /
- simple ω²-semigroup /
- Bruck-Reilly extension

HTML全文

参考文献(16)

[1]	REILLY N R. Bisimple ω-semigroups[J]. Proceedings of the Glasgow Mathematical Association, 1966(7): 160-167.
[2]	MUNN W D. Regular ω-semigroups[J]. Glasgow Mathematical Journal, 1968(9): 46-66.
[3]	WARNE R J. A characterization of certain regular d-classes in semigroups[J]. Illinois Mathematical Journal, 1965(9): 304-306.
[4]	WARNE R J. Bisimple inverse semigroups mod groups[J]. Duke Mathematical Journal, 1967(34): 787-811.
[5]	汪立民, 商宇. 正则双单ω²-半群[J]. 数学进展, 2008, 37(1): 121-122. WANG L M, SHANG Y. Regular bisimple ω²-semigroups[J]. Advances in Mathematics Journal, 2008, 37(1): 121-122.
[6]	商宇, 汪立民. 一类正则单ω²-半群-I[J]. 数学进展, 2013, 42(5): 631-643. SHANG Y, WANG L M. A class of regular simple ω²-semigroups-I[J]. Advances in Mathematics Journal, 2013, 42(5): 631-643.
[7]	商宇, 汪立民. 型A ω²-半群[J]. 数学进展, 2015, 44(4): 519-529. SHANG Y, WANG L M. Type A ω²-semigroups[J]. Advances in Mathematics Journal, 2015, 44(4): 519-529.
[8]	商宇, 冯莹莹, 汪立民. 正则ω²-半群[J]. 云南大学学报(自然科学版), 2018, 40(3): 415-422. SHANG Y, FENG Y Y, WANG L M. Regular ω²-semigroups[J]. Journal of Yunnan University(Natural Sciences Edition), 2018, 40(3): 415-422.
[9]	彭娇, 宫春梅. 幂等元集为正规带的r-宽大半群[J]. 云南大学学报(自然科学版), 2022, 44(5): 895-901. PENG J, GONG C M. r-wide semigroups whose idempotents form normal band[J]. Journal of Yunnan University(Natural Sciences Edition), 2022, 44(5): 895-901.
[10]	白雪娜, 宫春梅. 具有中间幂等元的r-宽大半群[J]. 云南大学学报(自然科学版), 2024, 46(1): 1-7. BAI X N, GONG C M. r-wide semigroups with medial idempotents[J]. Journal of Yunnan University(Natural Sciences Edition), 2024, 46(1): 1-7.
[11]	倪翔飞, 郭小江. 具有弱中间幂等元的正则半群[J]. 数学学报(中文版), 2018, 61(1): 107-122. NI X F, GUO X J. Regular semigroups with weak medial idempotents[J]. Acta Mathematica Sinica(Chinese Series), 2018, 61(1): 107-122.
[12]	EI-QALLALI A. Abundant semigroups with medial idempotents[J]. Categories and General Algebralc Structures with Applications Journal, 2021(15): 1-34.
[13]	刘海军, 郭小江. 左富足半群上的同余[J]. 数学进展, 2023, 52(2): 305-318. LIU H J, GUO X J. Congruences on left abundant semigroups[J]. Advances in Mathematics Journal, 2023, 52(2): 305-318.
[14]	LIU H J, GUO X J. Congruences on glrac semigroups(I)[J]. Journal Algebra Application, 2022, 21(12): 2250240/1-18.
[15]	HOWIE J M. Fundamentals of semigroup theory[M]. Oxford: Clarendon Press, 1995.
[16]	PETRICH M. Inverse semigroups[M]. New York: Wiley-Interscience, 1984.