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.
