Sur les elements bornants et les ideaux formes d'elements bornants joints dans les algebres bornologiques

Ahmed Zinedine, and Abdelaziz Tajmouati. "Sur les elements bornants et les ideaux formes d'elements bornants joints dans les algebres bornologiques." Commentationes Mathematicae 53.1 (2013): null. <http://eudml.org/doc/292407>.

@article{AhmedZinedine2013,
abstract = {Bounding elements and ideals consisting of joint bounding elements were essential tools in the study of permanent singularity in the class of all bornological algebras ([1], [6], [7], [8] and [12]). In this paper we give some important properties of these two notions. Especially, we compare boundings elements with some similar known notions such as bornological divisors of zero and topological divisors of zero. Then we show that these elements can be seen as algebraic divisor of zero in some suitable extension of the initial algebra. This result is analogous to a well-known result of Żelazko [11] concerning topological divisors of zero in Banach algebras. Finaly, we show that a maximal ideal is a prime ideal among ideals consisting of joint bounding elements. This is analougous to the result given in [4] concerning ideals consisting of joint topological divisors of zero in the case of Banach algebras.},
author = {Ahmed Zinedine, Abdelaziz Tajmouati},
journal = {Commentationes Mathematicae},
keywords = {permanently singular elements, bounding elements, non-removable ideals, ideals consisting of joint bounding elements},
language = {eng},
number = {1},
pages = {null},
title = {Sur les elements bornants et les ideaux formes d'elements bornants joints dans les algebres bornologiques},
url = {http://eudml.org/doc/292407},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Ahmed Zinedine
AU - Abdelaziz Tajmouati
TI - Sur les elements bornants et les ideaux formes d'elements bornants joints dans les algebres bornologiques
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 1
SP - null
AB - Bounding elements and ideals consisting of joint bounding elements were essential tools in the study of permanent singularity in the class of all bornological algebras ([1], [6], [7], [8] and [12]). In this paper we give some important properties of these two notions. Especially, we compare boundings elements with some similar known notions such as bornological divisors of zero and topological divisors of zero. Then we show that these elements can be seen as algebraic divisor of zero in some suitable extension of the initial algebra. This result is analogous to a well-known result of Żelazko [11] concerning topological divisors of zero in Banach algebras. Finaly, we show that a maximal ideal is a prime ideal among ideals consisting of joint bounding elements. This is analougous to the result given in [4] concerning ideals consisting of joint topological divisors of zero in the case of Banach algebras.
LA - eng
KW - permanently singular elements, bounding elements, non-removable ideals, ideals consisting of joint bounding elements
UR - http://eudml.org/doc/292407
ER -