Local algebras and the largest spectrum finite ideal.

Extracta Mathematicae (1998)

• Volume: 13, Issue: 1, page 61-67
• ISSN: 0213-8743

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Abstract

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M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of this last result by using the notion of local algebra attached to an element of an (associative, alternative or Jordan) algebra. Only the associative case will be considered here since there is no essential difference between the associative and the alternative cases.

How to cite

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Fernández López, Antonio, and Jaa, Omar. "Local algebras and the largest spectrum finite ideal.." Extracta Mathematicae 13.1 (1998): 61-67. <http://eudml.org/doc/38556>.

@article{FernándezLópez1998,
abstract = {M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of this last result by using the notion of local algebra attached to an element of an (associative, alternative or Jordan) algebra. Only the associative case will be considered here since there is no essential difference between the associative and the alternative cases.},
author = {Fernández López, Antonio, Jaa, Omar},
journal = {Extracta Mathematicae},
keywords = {Algebra de Banach; Ideales; Algebras de Jordan; socle; largest spectrum finite ideal; local algebra; semiprimitive alternative Banach complex algebra},
language = {eng},
number = {1},
pages = {61-67},
title = {Local algebras and the largest spectrum finite ideal.},
url = {http://eudml.org/doc/38556},
volume = {13},
year = {1998},
}

TY - JOUR
AU - Fernández López, Antonio
AU - Jaa, Omar
TI - Local algebras and the largest spectrum finite ideal.
JO - Extracta Mathematicae
PY - 1998
VL - 13
IS - 1
SP - 61
EP - 67
AB - M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of this last result by using the notion of local algebra attached to an element of an (associative, alternative or Jordan) algebra. Only the associative case will be considered here since there is no essential difference between the associative and the alternative cases.
LA - eng
KW - Algebra de Banach; Ideales; Algebras de Jordan; socle; largest spectrum finite ideal; local algebra; semiprimitive alternative Banach complex algebra
UR - http://eudml.org/doc/38556
ER -

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