# 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.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: LatticeProperties Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.