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 42 articles , 1 standard article )

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  1. Rezaei, Akbar: Pseudo-BCK algebras derived from directoids (2022)
  2. Aaly, Kologani M.; Rezaei, G. R.; Borzooei, R. A.; Jun, Y. B.: Hoops with quasi-valuation maps (2021)
  3. Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kologani, Mona Aaly; Jun, Young Bae: Soju filters in hoop algebras (2021)
  4. Ciungu, Lavinia Corina: Quantum B-algebras with involutions (2021)
  5. Ciungu, Lavinia Corina: Derivation operators on generalized algebras of BCK logic (2021)
  6. Ciungu, Lavinia Corina: Results in L-algebras (2021)
  7. Aaly Kologani, Mona; Borzooei, Rajab Ali: On ideal theory of hoops. (2020)
  8. Ciungu, Lavinia Corina: Monadic pseudo BE-algebras (2020)
  9. Aglianò, Paolo: Splittings in GBL-algebras. II: The representable case (2019)
  10. Aglianò, Paolo: Splittings in GBL-algebras. I: The general case (2019)
  11. Ciungu, Lavinia Corina: Involutive filters of pseudo-hoops (2019)
  12. Ciungu, Lavinia Corina: Commutative deductive systems of pseudo-BCK-algebras (2018)
  13. Ciungu, Lavinia Corina: State pseudo-equality algebras (2018)
  14. Emanovský, Petr; Kühr, Jan: Some properties of pseudo-BCK- and pseudo-BCI-algebras (2018)
  15. Ledda, Antonio; Paoli, Francesco; Tsinakis, Constantine: The Archimedean property: new horizons and perspectives (2018)
  16. Namdar, A.; Borzooei, R. A.: Nodal filters in hoop algebras (2018)
  17. Wang, Juntao; Xin, Xiaolong; He, Pengfei: Monadic bounded hoops (2018)
  18. Borzooei, R. A.; Varasteh, H. R.; Borna, K.; Radfar, A.: Results on hyper hoop-algebras (2017)
  19. Ceterchi, Rodica: The decomposition of linearly ordered pseudo-hoops (2017)
  20. He, Pengfei; Zhao, Bin; Xin, Xiaolong: States and internal states on semihoops (2017)

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