Left (Right) Regular and Transposition Regular Semigroups and Their Structures

Xiaohong Zhang and Yudan Du
Additional contact information
Xiaohong Zhang: School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China
Yudan Du: School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective: by transforming the positions of the elements in the regularity conditions, some new regularity conditions (collectively referred to as transposition regularity) are obtained, and the concepts of various transposition regular semigroups are introduced (L1/L2/L3, R1/R2/R3-transposition regular semigroups, etc.). Their relations with completely regular semigroups and left (right) regular semigroups, proposed by Clifford and Preston, are analyzed. Their properties and structures are studied from the aspects of idempotents, local identity elements, local inverse elements, subsemigroups and so on. Their decomposition theorems are proved respectively, and some new necessary and sufficient conditions for semigroups to become completely regular semigroups are obtained.

Keywords: regular semigroups; transposition regular semigroups; decomposition theorems; completely regular semigroups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1021/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1021/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1021-:d:776962

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().