Pseudo Hoops

 

Title: Pseudo Hoops
Authors: George Georgescu, Laurentiu Leustean and Viorel Preoteasa (viorel /dot/ preoteasa /at/ aalto /dot/ fi)
Submission date: 2011-09-22
Abstract: Pseudo-hoops are algebraic structures introduced by B. Bosbach under the name of complementary semigroups. In this formalization we prove some properties of pseudo-hoops and we define the basic concepts of filter and normal filter. The lattice of normal filters is isomorphic with the lattice of congruences of a pseudo-hoop. We also study some important classes of pseudo-hoops. Bounded Wajsberg pseudo-hoops are equivalent to pseudo-Wajsberg algebras and bounded basic pseudo-hoops are equivalent to pseudo-BL algebras. Some examples of pseudo-hoops are given in the last section of the formalization.
BibTeX:
@article{PseudoHoops-AFP,
  author  = {George Georgescu and Laurentiu Leustean and Viorel Preoteasa},
  title   = {Pseudo Hoops},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2011,
  note    = {\url{http://isa-afp.org/entries/PseudoHoops.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: LatticeProperties