Abundant semigroups with a multiplicative quasi-adequate transversal

2008 ◽  
Vol 78 (1) ◽  
pp. 34-53 ◽  
Author(s):  
Xiangfei Ni
Keyword(s):  
Abundant Semigroups ◽  
Adequate Transversal

Good congruences on abundant semigroups with quasi-ideal adequate transversals

2019 ◽  
Vol 56 (3) ◽  
pp. 323-334
Author(s):  
Aifa Wang
Keyword(s):  
Complete Lattice ◽  
Abundant Semigroup ◽  
Structure Component ◽  
Abundant Semigroups ◽  
Adequate Transversal

Abstract The aim of this paper is to study the congruences on abundant semigroups with quasi-ideal adequate transversals. The good congruences on an abundant semigroup with a quasi-ideal adequate transversal S° are described by the equivalence triple abstractly which consists of equivalences on the structure component parts I, S° and Λ. Also, it is shown that the set of all good congruences on this kind of semigroup forms a complete lattice.

Abundant semigroups with a quasi-ideal quasi-adequate transversal

2009 ◽  
Vol 25 (10) ◽  
pp. 1653-1664 ◽  
Author(s):  
Xiang Fei Ni ◽  
Yan Feng Luo ◽  
Hai Zhou Chao
Keyword(s):  
Abundant Semigroups ◽  
Adequate Transversal

scholarly journals The characterization and the product of quasi-Ehresmann transversals

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2051-2060
Author(s):  
Xiangjun Kong ◽  
Pei Wang
Keyword(s):  
Abundant Semigroup ◽  
Regular Semigroups ◽  
The Real ◽  
Abundant Semigroups

Wang (Filomat 29(5), 985-1005, 2015) introduced and investigated quasi-Ehresmann transversals of semi-abundant semigroups satisfy conditions (CR) and (CL) as the generalizations of orthodox transversals of regular semigroups in the semi-abundant case. In this paper, we give two characterizations for a generalized quasi-Ehresmann transversal to be a quasi-Ehresmann transversal. These results further demonstrate that quasi-Ehresmann transversals are the ?real? generalizations of orthodox transversals in the semi-abundant case. Moreover, we obtain the main result that the product of any two quasi-ideal quasi-Ehresmann transversals of a semi-abundant semigroup S which satisfy the certain conditions is a quasi-ideal quasi-Ehresmann transversal of S.

scholarly journals Semi-abundant semigroups with quasi-Ehresmann transversals

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 985-1005
Author(s):  
Shoufeng Wang
Keyword(s):  
Structure Theorem ◽  
Regular Semigroups ◽  
Abundant Semigroups

Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated orthodox transversals of regular semigroups. In this paper, we initiate the investigation of quasi-Ehresmann transversals of semi-abundant semigroups which are generalizations of orthodox transversals of regular semigroups. Some interesting properties associated with quasi-Ehresmann transversals are established. Moreover, a structure theorem of semi-abundant semigroups with generalized bi-ideal strong quasi-Ehresmann transversals is obtained. Our results generalize and enrich Chen?s results.

scholarly journals On Naturally Ordered Abundant Semigroups with an Adequate Monoid Transversal

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Wei Chen
Keyword(s):  
Structure Theorem ◽  
Abundant Semigroups

In this paper, we study a class of naturally ordered abundant semigroups with an adequate monoid transversal, namely, naturally ordered concordant semigroups with an adequate monoid transversal. After giving some properties of such semigroups, we obtain a structure theorem for naturally ordered concordant semigroups with an adequate monoid transversal.

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