The pseudo-hoops were originally introduced by Bosbach under the name of complementary semigroups. It was proved that a pseudo-hoop has the pseudo-divisibility condition and it is a meet-semilattice, so a bounded R-monoid can be viewed as a bounded pseudohoop together with the join-semilattice property. In other words, a bounded pseudohoop is a meet-semilattice ordered residuated, integral and divisible monoid.

In this chapter we present the main notions and results regarding the pseudo-hoops, we prove new properties of these structures, we introduce the notions of join-center and cancellative-center of pseudo-hoops and we define and study algebras on subintervals of pseudo-hoops.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lavinia Corina Ciungu
    • 1
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA

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