### 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.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session PseudoHoops

- Operations
- LeftComplementedMonoid
- RightComplementedMonoid
- PseudoHoops
- PseudoHoopFilters
- PseudoWaisbergAlgebra
- SpecialPseudoHoops
- Examples

### Depends on

- Lattice Properties

### Auto-related entries

- Extensions to the Comprehensive Framework for Saturation Theorem Proving

## Cite

×

PseudoHoops-AFP

    @article{PseudoHoops-AFP,
      author  = {George Georgescu and Laurentiu Leustean and Viorel Preoteasa},
      title   = {Pseudo Hoops},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2011},
      note    = {\url{https://isa-afp.org/entries/PseudoHoops.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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