Subsocles and direct sum of uniserial modules

Ayazul Hasan

doi:10.13069/jacodesmath.1000852

Subsocles and direct sum of uniserial modules

Abstract

Suppose $M$ is a $QTAG$-module with a subsocle $S$ such that $M/S$ is a direct sum of uniserial modules. Our global aim here is to investigate an interesting connection between the structure of $M/S$ and the $QTAG$-module $M$. Specifically, the condition $S=Soc(N)$ for some $h$-pure submodules $N$ of $M$ allows $M$ to inherit the structure of $M/S$.

Keywords

References

[1] M. Ahmad, A. H. Ansari, M. Z. Khan, On subsocles of S2-modules, Tamkang J. Math. 11(2) (1980) 221-229.
[2] A. Facchini, L. Salce, Uniserial modules: sums and isomorphisms of subquotients, Comm. Algebra 18(2) (1990) 499-517.
[3] L. Fuchs, Infinite Abelian groups, Volume I, Pure Appl. Math. 36, Academic Press, New York (1970).
[4] L. Fuchs, Infinite Abelian groups, Volume II, Pure Appl. Math. 36, Academic Press, New York (1973).
[5] A. Hasan, On essentially finitely indecomposable QTAG-modules, Afr. Mat. 27(1) (2016) 79-85.
[6] A. Hasan, Rafiquddin, On completeness in QTAG-modules, (Communicated).
[7] J. Irwin, J. Swanek, On purifiable subsocles of a primary Abelian group, Can. J. Math. 23(1) (1971) 48-57.
[8] M. Z. Khan, Torsion modules behaving like torsion Abelian groups, Tamkang J. Math. 9(1) (1978) 15-20.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Ayazul Hasan ^* This is me
0000-0002-2895-8267
Saudi Arabia

Publication Date

September 15, 2021

Submission Date

November 27, 2020

Acceptance Date

April 16, 2021

Published in Issue

Year 1970 Volume: 8 Number: 3

DOI

https://doi.org/10.13069/jacodesmath.1000852

IZ

https://izlik.org/JA22PJ66AR

Cite

RIS / Bibtex

APA

Hasan, A. (2021). Subsocles and direct sum of uniserial modules. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(3), 213-218. https://doi.org/10.13069/jacodesmath.1000852

AMA

1.Hasan A. Subsocles and direct sum of uniserial modules. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(3):213-218. doi:10.13069/jacodesmath.1000852

Chicago

Hasan, Ayazul. 2021. “Subsocles and Direct Sum of Uniserial Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications 8 (3): 213-18. https://doi.org/10.13069/jacodesmath.1000852.

EndNote

Hasan A (September 1, 2021) Subsocles and direct sum of uniserial modules. Journal of Algebra Combinatorics Discrete Structures and Applications 8 3 213–218.

IEEE

[1]A. Hasan, “Subsocles and direct sum of uniserial modules”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 3, pp. 213–218, Sept. 2021, doi: 10.13069/jacodesmath.1000852.

ISNAD

Hasan, Ayazul. “Subsocles and Direct Sum of Uniserial Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/3 (September 1, 2021): 213-218. https://doi.org/10.13069/jacodesmath.1000852.

JAMA

1.Hasan A. Subsocles and direct sum of uniserial modules. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:213–218.

MLA

Hasan, Ayazul. “Subsocles and Direct Sum of Uniserial Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 3, Sept. 2021, pp. 213-8, doi:10.13069/jacodesmath.1000852.

Vancouver

1.Ayazul Hasan. Subsocles and direct sum of uniserial modules. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021 Sep. 1;8(3):213-8. doi:10.13069/jacodesmath.1000852