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The diamond partial order in rings

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The diamond partial order in rings

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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

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Título: The diamond partial order in rings
Autor: Lebtahi Ep-Kadi-Hahifi, Leila Patricio, Pedro Thome, Néstor
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
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 ...[+]
Palabras clave: Star partial order , Minus partial order , Sharp partial order , Ring , Principal ideal
Derechos de uso: Reserva de todos los derechos
Fuente:
Linear and Multilinear Algebra. (issn: 0308-1087 ) (eissn: 1563-5139 )
DOI: 10.1080/03081087.2013.779272
Editorial:
Taylor & Francis: STM, Behavioural Science and Public Health Titles
Versión del editor: http://dx.doi.org/10.1080/03081087.2013.779272
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2010-18228/ES/PROPIEDADES MATRICIALES CON APLICACION A LA TEORIA DE CONTROL/
info:eu-repo/grantAgreement/FCT//PEst-C%2FMAT%2FUI0013%2F2011/
info:eu-repo/grantAgreement/UNLPam//049%2F11/
Descripción: 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
Agradecimientos:
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). ...[+]
Tipo: Artículo

References

Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452

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

Patrício P, Mendes Araujo C. Moore-Penrose invertibility in involutory rings: the caseaa†=bb†. Linear and Multilinear Algebra. 2010;58:445–452. [+]
Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452

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

Patrício P, Mendes Araujo C. Moore-Penrose invertibility in involutory rings: the caseaa†=bb†. Linear and Multilinear Algebra. 2010;58:445–452.

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

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

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

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

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

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

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

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