Pseudo Hoops

Pseudo Hoops. 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.

References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Ciungu, Lavinia Corina: Results in L-algebras (2021)
  2. Aaly Kologani, Mona; Borzooei, Rajab Ali: On ideal theory of hoops. (2020)
  3. Aglianò, Paolo: Splittings in GBL-algebras. II: The representable case (2019)
  4. Aglianò, Paolo: Splittings in GBL-algebras. I: The general case (2019)
  5. Ciungu, Lavinia Corina: Involutive filters of pseudo-hoops (2019)
  6. Ciungu, Lavinia Corina: State pseudo-equality algebras (2018)
  7. Ciungu, Lavinia Corina: Commutative deductive systems of pseudo-BCK-algebras (2018)
  8. Emanovský, Petr; Kühr, Jan: Some properties of pseudo-BCK- and pseudo-BCI-algebras (2018)
  9. Ledda, Antonio; Paoli, Francesco; Tsinakis, Constantine: The Archimedean property: new horizons and perspectives (2018)
  10. Namdar, A.; Borzooei, R. A.: Nodal filters in hoop algebras (2018)
  11. Wang, Juntao; Xin, Xiaolong; He, Pengfei: Monadic bounded hoops (2018)
  12. Borzooei, R. A.; Varasteh, H. R.; Borna, K.; Radfar, A.: Results on hyper hoop-algebras (2017)
  13. Ceterchi, Rodica: The decomposition of linearly ordered pseudo-hoops (2017)
  14. He, Pengfei; Zhao, Bin; Xin, Xiaolong: States and internal states on semihoops (2017)
  15. Botur, Michal; Dvurečenskij, Anatolij: On pseudo-BL-algebras and pseudo-hoops with normal maximal filters (2016)
  16. Dvurečenskij, Anatolij; Zahiri, Omid: Pseudo equality algebras: revision (2016)
  17. Botur, Michal; Paseka, Jan: Filters on some classes of quantum B-algebras (2015)
  18. Dvurečenskij, Anatolij: On a new construction of pseudo BL-algebras (2015)
  19. Borzooei, Rajab Ali; Aaly Kologani, Mona: Stabilizer topology of hoops (2014)
  20. Dvurečenskij, Anatolij; Kowalski, Tomasz: Kites and pseudo BL-algebras. (2014)

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