On two generalizations of perspective abelian groups

Andrey R. Chekhlov; Peter Danchev; Özgür Taşdemir

doi:10.24330/ieja.1966382

On two generalizations of perspective abelian groups

Abstract

In this paper, we are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in these two directions that can be viewed as improvements on their rather more complicated structures and properties.

Keywords

References

M. Altun and A. C. Ozcan, On internally cancellable rings, J. Algebra Appl., 16(6) (2017), 1750117 (12 pp).
B. Amini, A. Amini and E. Momtahan, Weakly perspective rings and modules, J. Algebra Appl., 18(1) (2019), 1950014 (9 pp).
S. Breaz, G. Calugareanu and Ph. Schultz, Modules with Dedekind finite endomorphism rings, Mathematica, 53(76)(1) (2011), 15-28.
G. Calugareanu, Morphic abelian groups, J. Algebra Appl., 9(2) (2010), 185-193.
G. Calugareanu and A. Chekhlov, On perspective Abelian groups, Comm. Algebra, 53(8) (2025), 3418-3429.
P. Crawley, The cancellation of torsion abelian groups in direct sums, J. Algebra, 2 (1965), 432-442.
L. Fuchs, Infinite Abelian Groups, vols. I-II, Acad. Press, New York-London, 1970-1973.
L. Fuchs, On a substitution property of modules, Monatsh. Math., 75 (1971), 198-204.

Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Andrey R. Chekhlov This is me
Russian Federation

Peter Danchev ^*
Bulgaria

Özgür Taşdemir
Türkiye

Early Pub Date

June 8, 2026

Publication Date

-

Submission Date

December 24, 2025

Acceptance Date

May 10, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.24330/ieja.1966382

IZ

https://izlik.org/JA85NS46GN

Cite

RIS / Bibtex

APA

Chekhlov, A. R., Danchev, P., & Taşdemir, Ö. (2026). On two generalizations of perspective abelian groups. International Electronic Journal of Algebra, Advanced Online Publication, 1-19. https://doi.org/10.24330/ieja.1966382

AMA

1.Chekhlov AR, Danchev P, Taşdemir Ö. On two generalizations of perspective abelian groups. IEJA. 2026;(Advanced Online Publication):1-19. doi:10.24330/ieja.1966382

Chicago

Chekhlov, Andrey R., Peter Danchev, and Özgür Taşdemir. 2026. “On Two Generalizations of Perspective Abelian Groups”. International Electronic Journal of Algebra, no. Advanced Online Publication: 1-19. https://doi.org/10.24330/ieja.1966382.

EndNote

Chekhlov AR, Danchev P, Taşdemir Ö (June 1, 2026) On two generalizations of perspective abelian groups. International Electronic Journal of Algebra Advanced Online Publication 1–19.

IEEE

[1]A. R. Chekhlov, P. Danchev, and Ö. Taşdemir, “On two generalizations of perspective abelian groups”, IEJA, no. Advanced Online Publication, pp. 1–19, June 2026, doi: 10.24330/ieja.1966382.

ISNAD

Chekhlov, Andrey R. - Danchev, Peter - Taşdemir, Özgür. “On Two Generalizations of Perspective Abelian Groups”. International Electronic Journal of Algebra. Advanced Online Publication (June 1, 2026): 1-19. https://doi.org/10.24330/ieja.1966382.

JAMA

1.Chekhlov AR, Danchev P, Taşdemir Ö. On two generalizations of perspective abelian groups. IEJA. 2026;:1–19.

MLA

Chekhlov, Andrey R., et al. “On Two Generalizations of Perspective Abelian Groups”. International Electronic Journal of Algebra, no. Advanced Online Publication, June 2026, pp. 1-19, doi:10.24330/ieja.1966382.

Vancouver

1.Andrey R. Chekhlov, Peter Danchev, Özgür Taşdemir. On two generalizations of perspective abelian groups. IEJA. 2026 Jun. 1;(Advanced Online Publication):1-19. doi:10.24330/ieja.1966382