PC-lattices: A Class of Bounded BCK-algebras

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...

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Bibliographic Details
Published inBulletin of the Section of Logic Vol. 47; no. 1; pp. 33 - 44
Main Authors Shoar, Sadegh Khosravi, Borzooei, Rajab Ali, Moradian, R., Radfar, Atefe
Format Journal Article
LanguageEnglish
Published Warsaw University of Łódź 2018
Subjects
19th century
Algebra
Boolean
Boolean algebra
Lattice theory
Lattices (mathematics)
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Summary: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.  
ISSN:0138-0680
2449-836X
DOI:10.18778/0138-0680.47.1.03