The Congruences on Regular Semigroups with Inverse Transversals Associated with Green's Relations

FENG Yingying; SHANG Yu

doi:10.6054/j.jscnun.2021081

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(5): 103-107. > DOI: 10.6054/j.jscnun.2021081

FENG Yingying, SHANG Yu. The Congruences on Regular Semigroups with Inverse Transversals Associated with Green's Relations[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(5): 103-107. DOI: 10.6054/j.jscnun.2021081

Citation:

PDF (1071 KB)

The Congruences on Regular Semigroups with Inverse Transversals Associated with Green's Relations

FENG Yingying^1, ,,
SHANG Yu²

1.
Department of Mathematics, Foshan University, Foshan 528000, China
2.
School of Mathematics and Statistics, Pu'er University, Pu'er 665000, China

More Information

Received Date: March 02, 2021
Available Online: November 10, 2021

Graphical Abstract

Abstract

Abstract

Let S be a regular semigroup with an inverse transversal. Following the study of the lifting property of ele-ments in the quotient semigroup of S and the lifting property of Green's relations in the homomorphic image of S, congruences on S generated by Green's relations and by restriction of Green's relations to the important subsemi-groups of S are investigated. The classes of semigroups related to these congruences are described.
- inverse transversal,
- Green's relations,
- congruence

FullText(HTML)

References (16)

References

[1]	BLYTH T S, MCFADDEN R B. Regular semigroups with a multiplicative inverse transversal[J]. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1982, 92(3/4): 253-270.
[2]	ARAUJO J, ARAUJO J P, BENTZ W, et al. A transversal property for permutation groups motivated by partial transformations[J]. Journal of Algebra, 2021, 573: 741-759. doi: 10.1016/j.jalgebra.2020.12.024
[3]	李春华, 汪立民, 范自柱. 具有乘法型B断面富足半群的结构[J]. 数学进展, 2014, 43(2): 232-242. LI C H, WANG L M, FAN Z Z. The structure of abundant semigroups with a multiplicative type B transversal[J]. Advances in Mathematics(China), 2014, 43(2): 232-242.
[4]	王守峰. 具有可乘逆断面的正则半群上的预同态和限制积[J]. 山东大学学报(理学版), 2017, 52(8): 90-93. WANG S F. Prehomomorphisms and restricted products of regular semigroups with a multiplicative inverse transversal[J]. Journal of Shandong University(Natural Science), 2017, 52(8): 90-93.
[5]	SAITO T. Construction of regular semigroups with inverse transversals[J]. Proceedings of the Edinburgh Mathemati-cal Society, 1989, 32(1): 16-23.
[6]	TANG X L. Regular semigroups with inverse transversals[J]. Semigroup Forum, 1997, 55: 24-32. doi: 10.1007/PL00005909
[7]	SAITO T. A note on regular semigroups with inverse transversals[J]. Semigroup Forum, 1986, 33: 149-152. doi: 10.1007/BF02573188
[8]	BLYTH T S, ALMEIDA SANTOS M H. A classification of inverse transversals[J]. Communications in Algebra, 2001, 29: 611-624. doi: 10.1081/AGB-100001527
[9]	HOWIE J M, LALLEMENT G. Certain fundamental congruence on a regular semigroup[J]. Glasgow Mathematical Journal, 1966, 7(3): 145-159.
[10]	PASTIJN F, PETRICH M. Congruences on regular semi-groups associated with Green's relations[J]. Bollettino della Unione Matematica Italiana, 1987(7): 591-603.
[11]	冯莹莹, 汪立民. 正则半群上与格林关系有关的同余[J]. 华南师范大学学报(自然科学版), 2006(2): 22-26. doi: 10.3969/j.issn.1000-5463.2006.02.004 FENG Y Y, WANG L M. Congruences on regular semi-groups related with Green's relations[J]. Journal of South China Normal University(Natural Science Edition), 2006(2): 22-26. doi: 10.3969/j.issn.1000-5463.2006.02.004
[12]	SAITO T. Construction of regular semigroups with inverse transversals[J]. Proceedings of the Edinburgh Mathemati-cal Society, 1989, 32(1): 41-51. doi: 10.1017/S0013091500006891
[13]	TANG X L, WANG L M. Congruences on regular semi-groups with inverse transversals[J]. Communications in Algebra, 1995, 23: 4157-4171. doi: 10.1080/00927879508825455
[14]	PETRICH M, REILLY N R. Completely regular semi-groups[M]. New York: Wiley, 1999.
[15]	FENG Y Y, WANG L M. $\mathcal{T}$ $\mathcal{K}$ °-network of regular semi-groups with inverse transversals[J]. Journal of Algebra, Number Theory: Advances and Applications, 2018, 19(1): 1-27. doi: 10.18642/jantaa_7100121892
[16]	朱凤林. 具有逆断面的正则半群若干问题研究[D]. 合肥: 中国科学技术大学, 2003. ZHU F L. Some studies on regular semigroups with inverse transversals[D]. Hefei: University of Science and Technology of China, 2003.

Cited By

Cited by

Periodical cited type(1)

刘海军. 一类广义正则半群的幺半群同余. 江西师范大学学报(自然科学版). 2024(05): 514-516 .

Other cited types(0)

Get Citation

PDF

XML

Article views (401) PDF downloads (54) Cited by(1)

Turn off MathJax

Article Contents

Abstract

References

The Congruences on Regular Semigroups with Inverse Transversals Associated with Green's Relations

Abstract

References

Cited by

Periodical cited type(1)

Other cited types(0)

Catalog

Export File

Citation

Format

Content