PC-lattices: A Class of Bounded BCK-algebras
Sadegh Khosravi Shoar; Rajab Ali Borzooei; R. Moradian; Atefe Radfar
Bulletin of the Section of Logic (2018)
- Volume: 47, Issue: 1
- ISSN: 0138-0680
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topSadegh Khosravi Shoar, et al. "PC-lattices: A Class of Bounded BCK-algebras." Bulletin of the Section of Logic 47.1 (2018): null. <http://eudml.org/doc/295528>.
@article{SadeghKhosraviShoar2018,
abstract = {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. },
author = {Sadegh Khosravi Shoar, Rajab Ali Borzooei, R. Moradian, Atefe Radfar},
journal = {Bulletin of the Section of Logic},
keywords = {PC-lattice; BCK-lattice; Involutory BCK-algebras; Bounded commutative BCK-algebras},
language = {eng},
number = {1},
pages = {null},
title = {PC-lattices: A Class of Bounded BCK-algebras},
url = {http://eudml.org/doc/295528},
volume = {47},
year = {2018},
}
TY - JOUR
AU - Sadegh Khosravi Shoar
AU - Rajab Ali Borzooei
AU - R. Moradian
AU - Atefe Radfar
TI - PC-lattices: A Class of Bounded BCK-algebras
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 1
SP - null
AB - 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.
LA - eng
KW - PC-lattice; BCK-lattice; Involutory BCK-algebras; Bounded commutative BCK-algebras
UR - http://eudml.org/doc/295528
ER -
References
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