On U-orthodox semigroups  

作　　者：SHUM Kar Ping 

机构地区：[1]Department of Mathematics, The University of Hong Kong

出　　处：《Science China Mathematics》2009年第2期329-350,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10671151);Natural Science Foundation of Shaanxi Province (Grant No. SJ08A06);partially by UGC (HK) (Grant No. 2160123)

摘　　要：As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semi-groups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in HU on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup WU and a V-ample semigroup (T,V ). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.

关 键 词：orthodox semigroups type W semigroups U-orthodox semigroups U-ample semigroups spined products 20M10 

分 类 号：O152.7[理学—数学]