On a generalization of $D3$-modules

Diop, Papa Cheikhou; Seye, Modou; Maurya, Sanjeev Kumar; Barry, Mamadou

Indian Journal of Mathematics

On a generalization of $D3$-modules

Author(s): Papa Cheikhou Diop Papa Cheikhou Diop Département de Mathematiques,
UFR Sciences et Technologies,
Université de Thiès,
Thiès, Sénégal. cheikh.diop@univ-thies.sn , Modou Seye Modou Seye Département de Mathematiques,
UFR Sciences et Technologies,
Université de Thiès,
Thiès, Sénégal. modou.seye@univ-thies.sn , Sanjeev Kumar Maurya Sanjeev Kumar Maurya Department of Mathematics,
School of Basic Sciences,
Galgotias University,Gautam Buddha Nagar,
India sanjeevm50@gmail.com , Mamadou Barry Mamadou Barry Département de mathématiques,
Faculté des sciences et techniques,
Université Cheikh Anta Diop,
Dakar Sénégal. mamadou.barry@ucad.edu.sn

Vol. 67, No. 1 (2025) • pp. 109–132

Published 27-04-2026 Article History Received 10-11-2025 Revised 06-02-2026 Published 27-04-2026

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Abstract

$ R $ is supposed to be an associative ring with identity and $ M $ be a unital left $R$-module. In this paper, we present the concept of a $D31$-module that generalizes the concept of a $D3$-module introduced in [14] and studied in [25] . A module $M$ is termed as $ D31 $-module if, whenever $ W $ and $ X $ are summands of $ M $ with $ W + X = M $ and $ W $ is cosingular, we have $ W \cap X $ is a direct summand of $ M $. We explore fundamental properties of these modules and establish that the class of rings $ R $ such that every $ D31 $-module is also a $ D3 $-module coincides precisely with the class of COSP-rings. Additionally, we examine the connections between $ D31 $-modules and other related module classes.

Keywords

Small submodules, cosingular modules, projective modules, $D3$-modules, $D31$-modules

2020 Mathematics Subject Classification

16D10, 16D40, 16D60, 16L30

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Allahabad Mathematical Society

On a generalization of $D3$-modules

Abstract

Keywords

2020 Mathematics Subject Classification

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