Pokaż uproszczony rekord

PC-lattices: A Class of Bounded BCK-algebras

dc.contributor.authorShoar, Sadegh Khosravi
dc.contributor.authorBorzooei, Rajab Ali
dc.contributor.authorMoradian, R.
dc.contributor.authorRadfar, Atefe
dc.date.accessioned2019-01-14T14:03:04Z
dc.date.available2019-01-14T14:03:04Z
dc.date.issued2018
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/26410
dc.description.abstractIn 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.en_GB
dc.language.isoenen_GB
dc.publisherWydawnictwo Uniwersytetu Łódzkiegoen_GB
dc.relation.ispartofseriesBulletin of the Section of Logic;1
dc.rightsThis work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.en_GB
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0en_GB
dc.subjectPC-latticeen_GB
dc.subjectBCK-latticeen_GB
dc.subjectInvolutory BCK-algebrasen_GB
dc.subjectBounded commutative BCK-algebrasen_GB
dc.titlePC-lattices: A Class of Bounded BCK-algebrasen_GB
dc.typeArticleen_GB
dc.page.number33-44
dc.contributor.authorAffiliationDepartment of Mathematics, Fasa University, Fasa, Iran
dc.contributor.authorAffiliationDepartment of Mathematics, Shahid Beheshti University, Tehran, Iran
dc.contributor.authorAffiliationDepartment of mathematics Farhangian University, Tehran, Iran
dc.contributor.authorAffiliationPayame Noor University, p. o. box. 19395-3697, Tehran, Iran
dc.identifier.eissn2449-836X
dc.referencesC. Bărbăcioru, Positive implicative BCK-algebras, Mathematica Japonica 36 (1967), pp. 11–59.en_GB
dc.referencesR. A. Borzooei, S. Khosravi Shoar, Implication Algebras are Equivalent to the Dual Implicative BCK-algebras, Scientiae Mathematicae Japonicae 633 (2006), pp. 429–431.en_GB
dc.referencesR. A. Borzooei, S. Khosravi Shoar, R. Ameri, Some new filters in MTL-algebras, Fuzzy Sets and Systems 187(1) (2012), pp. 92–102.en_GB
dc.referencesB. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 1990, 2002.en_GB
dc.referencesG. Grätzer, General Lattice Theory, Academic Press, 1978.en_GB
dc.referencesY. Huang, BCI-algebras, Science Press, 2006.en_GB
dc.referencesY. Huang, On involutory BCK-algebras, Soochow Journal of Mathematics 32(1) (2006), pp. 51–57.en_GB
dc.referencesY. Imai, K. Iséki, On axioms systems of propositional calculi XIV, Proceedings of the Japan Academy 42 (1966), pp. 19–22.en_GB
dc.referencesK. Iséki, BCK-algebras with condition (S), Mathematica Japonica 24 (1979), pp. 107–119.en_GB
dc.referencesK. lséki, On positive implicative BCK-algebras with condition (S), Mathematica Japonica 24 (1979), pp. 107–119.en_GB
dc.referencesK. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Mathematica Japonica 23 (1978), pp. 1–26.en_GB
dc.referencesJ. Meng and Y. B. Jun, BCK-Algebras, Kyung Moon Sa Co, Seoul, Korea, 1994.en_GB
dc.referencesS. Tanaka, A new class of algebras, Mathematics Seminar Notes 3 (1975), pp. 37–43.en_GB
dc.referencesS. Tanaka, On ^-commutative algebras, Mathematics Seminar Notes 3 (1975), pp. 59–64.en_GB
dc.contributor.authorEmailkhosravi.shoar@fasau.ac.ir
dc.contributor.authorEmailborzooei@sbu.ac.ir
dc.contributor.authorEmailRmoradian2017@gmail.com
dc.contributor.authorEmailradfar@pnu.ac.ir
dc.identifier.doi10.18778/0138-0680.47.1.03
dc.relation.volume47en_GB
dc.subject.msc06F35
dc.subject.msc03G25


Pliki tej pozycji

Thumbnail
Nazwa:
0_3_33-44 Shoar_Borzooei_Morad ...
Rozmiar:
140.2KB
Format:
PDF
Oglądaj/Otwórz

Pozycja umieszczona jest w następujących kolekcjach

Pokaż uproszczony rekord

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.