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The diamond partial order in rings

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The diamond partial order in rings

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dc.contributor.author Lebtahi Ep-Kadi-Hahifi, Leila es_ES
dc.contributor.author Patricio, Pedro es_ES
dc.contributor.author Thome, Néstor es_ES
dc.date.accessioned 2016-01-26T15:41:53Z
dc.date.available 2016-01-26T15:41:53Z
dc.date.issued 2014
dc.identifier.issn 0308-1087
dc.identifier.uri http://hdl.handle.net/10251/60194
dc.description This is an author's accepted manuscript of an article published in " Linear and Multilinear Algebra"; Volume 62, Issue 3, 2014; copyright Taylor & Francis; available online at: http://dx.doi.org/10.1080/03081087.2013.779272 es_ES
dc.description.abstract In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran’s theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157–169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyse successors, predecessors and maximal elements under the diamond order. es_ES
dc.description.sponsorship The first and third authors have been partially supported by Ministry of Education of Spain, grant DGI MTM2010-18228 and the third one by Universidad Nacional de La Pampa, Facultad de Ingenieria (grant Resol. No 049/11). The second author was financed by FEDER Funds through 'Programa Operacional Factores de Competitividade - COMPETE' and by Portuguese Funds through FCT - 'Fundacao para a Ciencia e a Tecnologia', within the project PEst-C/MAT/UI0013/2011. en_EN
dc.language Inglés es_ES
dc.publisher Taylor & Francis: STM, Behavioural Science and Public Health Titles es_ES
dc.relation.ispartof Linear and Multilinear Algebra es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Star partial order es_ES
dc.subject Minus partial order es_ES
dc.subject Sharp partial order es_ES
dc.subject Ring es_ES
dc.subject Principal ideal es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title The diamond partial order in rings es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1080/03081087.2013.779272
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-18228/ES/PROPIEDADES MATRICIALES CON APLICACION A LA TEORIA DE CONTROL/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/FCT//PEst-C%2FMAT%2FUI0013%2F2011/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UNLPam//049%2F11/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Lebtahi Ep-Kadi-Hahifi, L.; Patricio, P.; Thome, N. (2014). The diamond partial order in rings. Linear and Multilinear Algebra. 62(3):386-395. https://doi.org/10.1080/03081087.2013.779272 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1080/03081087.2013.779272 es_ES
dc.description.upvformatpinicio 386 es_ES
dc.description.upvformatpfin 395 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 62 es_ES
dc.description.issue 3 es_ES
dc.relation.senia 237033 es_ES
dc.identifier.eissn 1563-5139
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Fundação para a Ciência e a Tecnologia, Portugal es_ES
dc.contributor.funder Universidad Nacional de La Pampa, Argentina es_ES
dc.description.references Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452 es_ES
dc.description.references Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9 es_ES
dc.description.references Patrício P, Mendes Araujo C. Moore-Penrose invertibility in involutory rings: the caseaa†=bb†. Linear and Multilinear Algebra. 2010;58:445–452. es_ES
dc.description.references Blackwood, B., Jain, S. K., Prasad, K. M., & Srivastava, A. K. (2009). Shorted Operators Relative to a Partial Order in a Regular Ring. Communications in Algebra, 37(11), 4141-4152. doi:10.1080/00927870902828629 es_ES
dc.description.references Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8 es_ES
dc.description.references Baksalary, J. K., Baksalary, O. M., Liu, X., & Trenkler, G. (2008). Further results on generalized and hypergeneralized projectors. Linear Algebra and its Applications, 429(5-6), 1038-1050. doi:10.1016/j.laa.2007.03.029 es_ES
dc.description.references Hauke, J., Markiewicz, A., & Szulc, T. (2001). Inter- and extrapolatory properties of matrix partial orderings. Linear Algebra and its Applications, 332-334, 437-445. doi:10.1016/s0024-3795(01)00294-4 es_ES
dc.description.references Mosić, D., & Djordjević, D. S. (2012). Some results on the reverse order law in rings with involution. Aequationes mathematicae, 83(3), 271-282. doi:10.1007/s00010-012-0125-2 es_ES
dc.description.references Mosić, D., & Djordjević, D. S. (2011). Further results on the reverse order law for the Moore–Penrose inverse in rings with involution. Applied Mathematics and Computation, 218(4), 1478-1483. doi:10.1016/j.amc.2011.06.040 es_ES
dc.description.references Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052 es_ES


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