TOPOLOGICALLY NOETHERIAN BANACH ALGEBRAS

被引：0
|
作者：
Mabrouk, M. [1 ,2 ]
Saeed, E. [2 ]
机构：
[1] Univ Sfax, Dept Math, Fac Sci Sfax, Sfax, Tunisia
[2] Umm Al Qura Univ, Dept Math, Fac Appl Sci, Mecca 21955, Saudi Arabia
来源：
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2023年 / 62卷 / 01期
关键词：
Banach algebra; topologically Noetherian; chain conditions;
D O I：
10.17654/0972555523018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Banach algebra 9t is said to be topologically left Noetherian (TLN) if for any increasing chain of closed left ideals I1 subset of I2 subset of MIDLINE HORIZONTAL ELLIPSIS, there exists an n is an element of N such that Im = In for all m >= n. We study some basic properties of this class of Banach algebras. In particular, we show that if 9t has an essential socle, then it is of finite dimension.
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页码：1 / 11
页数：11
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