Mathematics and Statistics Vol. 11(6), pp. 917 - 922
DOI: 10.13189/ms.2023.110606
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Σ-uniserial Modules and Their Properties

Ayazul Hasan ^1,*, Jules Clement Mba ^2
1 College of Applied Industrial Technology, Jazan University, Kingdom of Saudi Arabia
² School of Economics, College of Business and Economics, University of Johannesburg, South Africa

ABSTRACT

The close association of abelian group theory and the theory of modules have been extensively studied in the literatures. In fact, the theory of abelian groups is one of the principal motives of new research in module theory. As it is well-known, module theory can only be processed by generalizing the theory of abelian groups that provide novel viewpoints of various structures for torsion abelian groups. The theory of torsion abelian groups is significant as it generates the natural problems in QTAG-module theory. The notion of QTAG (torsion abelian group like) module is one of the most important tools in module theory. Its importance lies behind the fact that this module can be applied in order to generalized torsion abelian group accurately. Significant work on QTAG-module was produced by many authors, concentrating on establishing when torsion abelian groups are actually QTAG-modules. There are two rather natural problems which arise in connection with the Σ-uniserial modules. Namely: The QTAG-module M is Σ-uniserial if and only if all N-high submodules of M are Σ-uniserial, for some basic submodules N of M, and M is not a Σ-uniserial module if and only if it contains a proper (ω + 1)-projective submodule. The current work explores these two problems for QTAG-modules. Some related concepts and problems are also considered. Our global aim here is to review the relationship between the aspects of group theory in the form of torsion abelian groups and theory of modules in the form of QTAG-modules.

KEYWORDS
QTAG-modules, Σ-uniserial Modules, N-high Submodules

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ayazul Hasan , Jules Clement Mba , "Σ-uniserial Modules and Their Properties," Mathematics and Statistics, Vol. 11, No. 6, pp. 917 - 922, 2023. DOI: 10.13189/ms.2023.110606.

(b). APA Format:
Ayazul Hasan , Jules Clement Mba (2023). Σ-uniserial Modules and Their Properties. Mathematics and Statistics, 11(6), 917 - 922. DOI: 10.13189/ms.2023.110606.