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dc.contributor.author
Corach, Gustavo
dc.contributor.author
Duggal, Bhaggy
dc.contributor.author
Harte, Robin
dc.date.available
2016-01-04T20:04:30Z
dc.date.issued
2013-01
dc.identifier.citation
Corach, Gustavo; Duggal, Bhaggy ; Harte, Robin; Extensions of Jacobson's Lemma; Taylor; Communications In Algebra; 41; 1-2013; 520-531
dc.identifier.issn
0092-7872
dc.identifier.uri
http://hdl.handle.net/11336/3306
dc.description.abstract
Jacobson’s Lemma says that if a c ∈ A thenac − 1 ∈ A−1 ⇐⇒ ca − 1 ∈ A−1 which holds separately for the left and the right invertibles of A, as well as for the non zero-divisors of A. In this note, we generalize the identity above and many of its relatives from ca − 1 to certain ba − 1: specifically we will suppose aba = aca. Three special cases are of interest: the case b = c which will give Jacobson’s lemma; the case in which aba = aca = a in which both b and c are generalized inverses of a ∈ A; and the case aba = a^2 in which c = 1. This last case goes back to Vidav; in particular, Schmoeger shows that aba=a^2 holds if there are idempotents p = p^2 q = q^2 for which a = qp and b = pq. The central results in this note are of course pure algebra: but in the neighboring realm of topological algebra they have very close relatives, and we take the opportunity to extend our purely algebraic observations to their topological analogues.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Taylor
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Jacobson'S Lemma
dc.subject
Operator
dc.subject
Resolvent
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Extensions of Jacobson's Lemma
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-03-30 10:35:44.97925-03
dc.journal.volume
41
dc.journal.pagination
520-531
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Londres
dc.description.fil
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
dc.description.fil
Fil: Duggal, Bhaggy . Visegradska. Faculty of Science and Mathematics. Department of Mathematics; Serbia
dc.description.fil
Fil: Harte, Robin. Universidad de Dublin; Irlanda
dc.journal.title
Communications In Algebra
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2011.602274
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http:/dx.doi.org/10.1080/00927872.2011.602274
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