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The structure of ℒ*-inverse semigroups

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Abstract

The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products.

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Authors and Affiliations

  1. Department of Mathematics, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Ren Xueming

  2. Faculty of Science, The Chinese University of Hong Kong, Hong Kong, China

    Shum Karping

Authors
  1. Ren Xueming
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  2. Shum Karping
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Correspondence to Ren Xueming or Shum Karping.

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Ren, X., Shum, K. The structure of ℒ*-inverse semigroups. SCI CHINA SER A 49, 1065–1081 (2006). https://doi.org/10.1007/s11425-006-1065-x

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  • DOI: https://doi.org/10.1007/s11425-006-1065-x

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