Geodesic
PC-lattices: A Class of Bounded BCK-algebras
Bulletin of the Section of Logic, Tome 47 (2018) no. 1.

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In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice with condition (S) is a distributive BCK-algebra.  
Keywords: PC-lattice, BCK-lattice, Involutory BCK-algebras, Bounded commutative BCK-algebras 
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     author = {Shoar, Sadegh Khosravi and Borzooei, Rajab Ali and Moradian, R. and Radfar, Atefe},
     title = {PC-lattices: {A} {Class} of {Bounded} {BCK-algebras}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2018_47_1_a3/}
}
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Shoar, Sadegh Khosravi; Borzooei, Rajab Ali; Moradian, R.; Radfar, Atefe. PC-lattices: A Class of Bounded BCK-algebras. Bulletin of the Section of Logic, Tome 47 (2018) no. 1. http://geodesic.mathdoc.fr/item/BSL_2018_47_1_a3/