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Lattice Characteristics of Classes of Semigroups

  • Lev N. Shevrin
  • Alexander J. Ovsyannikov
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 379)

Abstract

We say that a class A of semigroups is lattice-characterized if one can indicate conditions formulated in lattice-theoretic terms such that the lattice SubS of a semigroup S satisfies these conditions if and only if S ∈ A; such conditions will be called a lattice characteristic of a class A. Speaking about lattice-theoretic conditions, we mean abstract properties (i.e. inherited by isomorphic images) so each lattice-characterized class is clearly abstract. If all semigroups in such a class A are isomorphic, i.e., in other words, A consists, up to isomorphism, of a single semigroup, say A, then we say that the semigroup A is lattice-characterized.

Keywords

Lattice Characteristic Finite Order Infinite Order Semi Group Finite Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Lev N. Shevrin
    • 1
  • Alexander J. Ovsyannikov
    • 1
  1. 1.Department of MathematicsUral State UniversityEkatarinburgRussia

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