Pseudo-BCK algebras and PD-posets
The notion of pseudo-BCK algebras was introduced by Georgescu and Iorgulescu Proceedings of DMTCS'01: Combinatorics, Computability and Logic, Springer, London, pp 97-114, 2001. It is so general that fleas, pseudo-hoops, psMTL, psBL, pseudo-MV et al., and so hoops, MTL, BL, MV et al. can be seen its extensions. In this paper, we extend the ideal and congruence theory to pseudo-BCK algebras, and investigate the connections between pseudo-BCK algebras and PD(GPD)-posets.
pseudo-bck algebra pd-poset ideal congruence normal ideal prime ideal