On regularly coherent modules and regularly Noetherian modules
Abstract
The concepts of regular Noetherianity and regular coherence, which extend the classical notions of Noetherian and coherent rings, have been fundamental in the study of algebraic structures. In this paper, we aim to expand these notions to the realm of module theory. Specifically, we introduce and explore weak versions of injective, flat, and projective modules, which we term as reg-injective, reg-flat, and reg-projective modules. We provide analogues of classical results and establish their properties, offering examples to illustrate modules that meet these new criteria but not their classical counterparts. Additionally, we define and study regularly Noetherian and regularly coherent modules, characterizing their properties and examining their stability under various ring constructions. Our results contribute new examples and broaden the current understanding of these algebraic concepts.
Keywords
References
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Details
Primary Language
English
Subjects
Algebra and Number Theory
Journal Section
Research Article
Early Pub Date
August 16, 2025
Publication Date
January 10, 2026
Submission Date
February 4, 2025
Acceptance Date
June 2, 2025
Published in Issue
Year 2026 Volume: 39 Number: 39
APA
El Haddaoui, Y., Kım, H., & Mahdou, N. (2026). On regularly coherent modules and regularly Noetherian modules. International Electronic Journal of Algebra, 39(39), 143-169. https://doi.org/10.24330/ieja.1767099
AMA
1.El Haddaoui Y, Kım H, Mahdou N. On regularly coherent modules and regularly Noetherian modules. IEJA. 2026;39(39):143-169. doi:10.24330/ieja.1767099
Chicago
El Haddaoui, Younes, Hwankoo Kım, and Najib Mahdou. 2026. “On Regularly Coherent Modules and Regularly Noetherian Modules”. International Electronic Journal of Algebra 39 (39): 143-69. https://doi.org/10.24330/ieja.1767099.
EndNote
El Haddaoui Y, Kım H, Mahdou N (January 1, 2026) On regularly coherent modules and regularly Noetherian modules. International Electronic Journal of Algebra 39 39 143–169.
IEEE
[1]Y. El Haddaoui, H. Kım, and N. Mahdou, “On regularly coherent modules and regularly Noetherian modules”, IEJA, vol. 39, no. 39, pp. 143–169, Jan. 2026, doi: 10.24330/ieja.1767099.
ISNAD
El Haddaoui, Younes - Kım, Hwankoo - Mahdou, Najib. “On Regularly Coherent Modules and Regularly Noetherian Modules”. International Electronic Journal of Algebra 39/39 (January 1, 2026): 143-169. https://doi.org/10.24330/ieja.1767099.
JAMA
1.El Haddaoui Y, Kım H, Mahdou N. On regularly coherent modules and regularly Noetherian modules. IEJA. 2026;39:143–169.
MLA
El Haddaoui, Younes, et al. “On Regularly Coherent Modules and Regularly Noetherian Modules”. International Electronic Journal of Algebra, vol. 39, no. 39, Jan. 2026, pp. 143-69, doi:10.24330/ieja.1767099.
Vancouver
1.Younes El Haddaoui, Hwankoo Kım, Najib Mahdou. On regularly coherent modules and regularly Noetherian modules. IEJA. 2026 Jan. 1;39(39):143-69. doi:10.24330/ieja.1767099