In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enric...In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.展开更多
A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particu...A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition （C） with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.展开更多
基金Supported by the Natural Science Foundation Project of Yunnan Education Department (Grant No.09Y0141)a Ph.D Foundation of Yunnan Normal University
文摘In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.
基金The research is supported by the Natural Science Foundation of China （11471255, 61672416）, Special Research Fundation of Education Department of Shaanxi Province （15JK1411）, Natural Science Basic Research Project in Shaanxi Province of China （2015JQ1006） and Basic Research Foundation of Xi＇an University of Architecture and Technology （JC1416）.
文摘A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition （C） with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.
