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algebra universalis

, Volume 44, Issue 3–4, pp 217–239 | Cite as

Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands

  • Norman R. Reilly
  • Shuhua Zhang

Abstract.

It has been shown by the authors that the mapping\(\chi : {\bf V} \longrightarrow {\bf V}\cap{\bf B}\),where B is the pseudovariety of finite bands, is a complete retraction of the lattice L(F) of pseudovarieties of finite semigroups onto the lattice of pseudovarieties of bands. It follows that the classes of the induced congruence \(\overline{\chi}\) on L(F), or on the lattice of subpseudovarieties L(W) for any subpseudovariety W of F, are intervals. In this paper we solve the membership problem for the upper limit of the classes of \(\overline{\chi}\) restricted to L(W) for various \({\bf W} \in {\bf L(F)}\), including F itself, and provide bases of pseudoidentities for certain cases.

Keywords

Membership Problem Finite Semigroup Finite Band 
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Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • Norman R. Reilly
    • 1
  • Shuhua Zhang
    • 1
  1. 1.Department of Mathematics and Statistics, Simon Fraser University,Burnaby BC V5A 1S6, Canada, e-mail: nreilly@cs.sfu.caCA

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