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dc.contributor.author
Cornejo, Juan Manuel
dc.contributor.author
Sankappanavar, Hanamantagouda P.
dc.date.available
2019-10-16T17:44:02Z
dc.date.issued
2018-07
dc.identifier.citation
Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; Symmetric implication zroupoids and identities of Bol–Moufang type; Springer; Soft Computing - (Print); 22; 13; 7-2018; 4319-4333
dc.identifier.issn
1472-7643
dc.identifier.uri
http://hdl.handle.net/11336/86022
dc.description.abstract
An algebra A= ⟨ A, → , 0 ⟩ , where → is binary and 0 is a constant, is called an implication zroupoid (I-zroupoid, for short) if A satisfies the identities: (I): (x→y)→z≈((z′→x)→(y→z)′)′, and (I0): 0 ′ ′≈ 0 , where x′: = x→ 0. An implication zroupoid is symmetric if it satisfies the identities: x′ ′≈ x and (x→y′)′≈(y→x′)′. An identity is of Bol–Moufang type if it contains only one binary operation symbol, one of its three variables occurs twice on each side, each of the other two variables occurs once on each side, and the variables occur in the same (alphabetical) order on both sides of the identity. In this paper, we will present a systematic analysis of all 60 identities of Bol–Moufang type in the variety S of symmetric I-zroupoids. We show that 47 of the subvarieties of S, defined by the identities of Bol–Moufang type, are equal to the variety SL of ∨ -semilattices with the least element 0 and one of others is equal to S. Of the remaining 12, there are only three distinct ones. We also give an explicit description of the poset of the (distinct) subvarieties of S of Bol–Moufang type.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
SYMMETRIC IMPLICATION ZROUPOID
dc.subject
IDENTIFICATION OF BOL-MOUFANG TYPE
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Symmetric implication zroupoids and identities of Bol–Moufang type
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-10-09T14:17:02Z
dc.identifier.eissn
1433-7479
dc.journal.volume
22
dc.journal.number
13
dc.journal.pagination
4319-4333
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.description.fil
Fil: Sankappanavar, Hanamantagouda P.. University of New York; Estados Unidos
dc.journal.title
Soft Computing - (Print)
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00500-017-2869-z
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00500-017-2869-z
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