On <Emphasis Type="Italic">U</Emphasis>-orthodox semigroups |
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Authors: | XueMing Ren YanHui Wang Kar Ping Shum |
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Institution: | (1) Department of Mathematics, Xi’an University of Architecture and Technology, Xi’an, 710055, China;(2) Department of Mathematics, The University of Hong Kong, Hong Kong(SAR), China |
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Abstract: | 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.
This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation
of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123) |
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Keywords: | orthodox semigroups type W semigroups U-orthodox semigroups U-ample semigroups spined products |
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