On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules

Dung Banh Duc

doi:10.47000/tjmcs.1689839

On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules

Abstract

The objective of this paper is to study the question of when modules have ADS$^{\circledast}$-preenvelopes and covers. It is proved that every ADS$^{\circledast}$ module over a ring $R$ is projective if and only if every right $R$-module has an ADS$^{\circledast}$-(pre)envelope (an ADS$^{\circledast}$-(pre)cover). We also introduce a generalization of ADS$^{\circledast}$ modules in terms of their invariance under certain automorphisms of their envelopes.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Dung Banh Duc ^*
0000-0003-1376-2867
Vietnam

Publication Date

February 23, 2026

Submission Date

May 2, 2025

Acceptance Date

June 27, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1689839

IZ

https://izlik.org/JA47ER43EE

Cite

RIS / Bibtex

APA

Banh Duc, D. (2026). On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules. Turkish Journal of Mathematics and Computer Science, 18(1), 1-10. https://doi.org/10.47000/tjmcs.1689839

AMA

1.Banh Duc D. On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules. TJMCS. 2026;18(1):1-10. doi:10.47000/tjmcs.1689839

Chicago

Banh Duc, Dung. 2026. “On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes Modules”. Turkish Journal of Mathematics and Computer Science 18 (1): 1-10. https://doi.org/10.47000/tjmcs.1689839.

EndNote

Banh Duc D (February 1, 2026) On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules. Turkish Journal of Mathematics and Computer Science 18 1 1–10.

IEEE

[1]D. Banh Duc, “On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules”, TJMCS, vol. 18, no. 1, pp. 1–10, Feb. 2026, doi: 10.47000/tjmcs.1689839.

ISNAD

Banh Duc, Dung. “On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes Modules”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 1-10. https://doi.org/10.47000/tjmcs.1689839.

JAMA

1.Banh Duc D. On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules. TJMCS. 2026;18:1–10.

MLA

Banh Duc, Dung. “On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes Modules”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 1-10, doi:10.47000/tjmcs.1689839.

Vancouver

1.Dung Banh Duc. On ADS$^{\circledast}$-(pre)covers and ADS$^{\circledast}$-(pre)envelopes modules. TJMCS. 2026 Feb. 1;18(1):1-10. doi:10.47000/tjmcs.1689839