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

• Autorzy: Ahmed Zinedine , Abdelaziz Tajmouati
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

permanently singular elements, bounding elements, non-removable ideals, ideals consisting of joint bounding elements

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: 53
• Numer: 1

Daty

wydano

2013

online

2013-06-15

Twórcy

autor

Ahmed Zinedine

autor

Abdelaziz Tajmouati

Identyfikatory

DOI

10.14708/cm.v53i1.777