Acta Mathematica Sinica

, Volume 17, Issue 3, pp 437–454

Morita Equivalence for Factorisable Semigroups

ORIGINAL ARTICLES

DOI: 10.1007/s101140000056

Cite this article as:
Chen, Y.Q. & Shum, K.P. Acta Math Sinica (2001) 17: 437. doi:10.1007/s101140000056

Abstract

Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context (S, R.,SPR,RQS,〈〉 , ⌈⌉) with 〈〉 and ⌈⌉ surjective. For a factorisable semigroup S, we denote ζS = {(s1, s2) ∈S×S|ss1 = ss2, ∀sS}, S' = SS and US-FAct = {SMS− Act |SM = M and SHomS(S, M) ≅M}. We show that, for factorisable semigroups S and M, the categories US-FAct and UR-FAct are equivalent if and only if the semigroups S' and R' are strongly Morita equivalent. Some conditions for a factorisable semigroups to be strongly Morita equivalent to a sandwich semigroup, local units semigroup, monoid and group separately are also given. Moreover, we show that a semigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I, SSHomS(S, ∐i∈IS) →∐i∈IS, st·ƒ↦ (st)ƒ is an S-isomorphism.

Keywords

CategoryS-actsFactorisable semigroupMorita equivalence

MR (2000) Subject Classification

20M50

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  1. 1.Department of MathematicsSouth China Normal UniversityGuangzhou 510631P. R. China
  2. 2.Department of MathematicsThe Chinese University of Hong KongShatinN.T., Hong Kong