On (ɱ,ɳ)-Strongly Fully Stably Banach Algebra Modules Related to an Ideal of Am ×ɳ

Authors

Radhi Ibraheem Mohammed Ali, Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq.Follow
Muna Jasim Mohammed Ali, Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq.Follow
Samira Naji Kadhim, Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq.Follow

Abstract

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-modulerelated to an ideal. Some properties of (ɱ,ɳ)-strong full stability B-Algebra-modulerelated to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-modulerelated to an ideal that states, a B-Ạ-module Ӽis (ɱ,ɳ)-strong full stability B-Algebra-modulerelated to an idealῌ, if and only if for any two ɱ-element sub-sets {Ṋẋ1,Ṋẋ1,ẋ2,⋯,Ṋẋ1,ẋ2,⋯,ẋɳ}and {Ḿỳ1,Ḿỳ1,ỳ2,⋯,Ḿỳ1,ỳ2,⋯,ỳɳ}of Ӽɳ, if ����∉∑������∩Ӽɱῌ����=1, for each j = 1, ..., ɱ, i = 1,..., ɳ����∈{Ṋẋ1,Ṋẋ1,ẋ2,⋯,Ṋẋ1,ẋ2,⋯,ẋɳ}and ����∈{Ḿỳ1,Ḿỳ1,ỳ2,⋯,Ḿỳ1,ỳ2,⋯,ỳɳ}implies��Ạɳ({Ṋẋ1,Ṋẋ1,ẋ2,⋯,Ṋẋ1,ẋ2,⋯,ẋɳ}) ⊈��Ạɳ({Ḿỳ1,Ḿỳ1,ỳ2,⋯,Ḿỳ1,ỳ2,⋯,ỳɳ})have been proved

Keywords

Fully-stable-B-algebra-module relate to an ideal, (M, N)-full-stability-B- Algebra-module relate to ideal, Multiplication-(ɱ, ɳ)-B-algebra-module relate to ideal, Baer-(ɱ, ɳ)-criterion relate to an ideal, Pure-(ɱ, ɳ)- sub-module .

Article Type

Article

How to Cite this Article

Ali, Radhi Ibraheem Mohammed; Ali, Muna Jasim Mohammed; and Kadhim, Samira Naji (2021) "On (ɱ,ɳ)-Strongly Fully Stably Banach Algebra Modules Related to an Ideal of Am ×ɳ," Baghdad Science Journal: Vol. 18: Iss. 4, Article 15.
DOI: https://doi.org/10.21123/bsj.2021.18.4.1234