Pseudo-BCK algebras and PD-posets |
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| Authors: | Yong Lin Liu San Yang Liu Yang Xu |
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| Affiliation: | (1) Department of Mathematics, Nanping Teachers College, Wuyishan, Fujian, 354300, People’s Republic of China;(2) Department of Mathematics, Xidian University, Xi’an, Shaanxi, 710071, People’s Republic of China;(3) Department of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People Republic of China |
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| Abstract: | 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. |
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| Keywords: | Pseudo-BCK algebra Ideal Congruence Normal ideal Prime ideal PD-poset |
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