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WE-m semigroups

  • Attila Nagy
Chapter
Part of the Advances in Mathematics book series (ADMA, volume 1)

Abstract

In this chapter we deal with semigroups in which, for every elements a and b, there is a non-negative integer k such that (ab) m+k =a m b m =(ab) k a m b m , where m is a fixed i n te g er m ≥ 2. These se m igrou p s are c a lled WE- m se m igroups. It is clear that every E-m semigroup is a WE-m semigroup. The examination of WE-m semigroups need some results about E-m semigroups. Thus the E-m semigroups were examined in the previous chapter. As a WE-m semigroup is a left and right Putcha semigroup, it is a semilattice of WE-m archimedean semigroups. We show that the 0-simple WE-mn semigroups are the completely simple E-m semigroups with a zero adjoined. A semigroup is a WE-m archimedean semigroup containing at least one idempotent element if and only if it is a retract extension of a completely simple E-m semigroup by a nil semigroup. We also prove that every WE-2 archimnedean semigroup without idempotent element has a non-trivial group homomorphic image. We deal with the regular WE-m semigroups. We show that the regular WE-m semigroups are exactly the regular exponential semigroups. Moreover, we show that a semigroup which is an ideal extension of a regular semigroup K by a nil sernigroup N is a WE-2 semigroup if and only if K is an E-2 semigroup and the extension is retract. We deal with the subdirectly irreducible WE-2 semigroups.

Keywords

Abelian Group Arbitrary Element Regular Semigroup Idempotent Element Ideal Extension 
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 2001

Authors and Affiliations

  • Attila Nagy
    • 1
  1. 1.Department of Algebra, Institute of MathematicsBudapest University of Technology and EconomicsHungary

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