T-Closed-Coessential and T-Closed-Coclosed Submodules

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DOI: https://doi.org/10.28924/2291-8639-23-2025-299
Published: Nov 28, 2025
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Mohammed Khalid Shahoodh, Omar Kareem Ali, T-Closed-Coessential and T-Closed-Coclosed Submodules, Int. J. Anal. Appl., 23 (2025), 299.

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Mohammed Khalid Shahoodh, Omar Kareem Ali

Abstract

Many generalizations have been provided in the field of abstract algebra specially in modules theory in order to presents some new concepts and study some of their properties. The goal of this article is to present new concepts of submodules as a generalization of previous studies. In particular, we provided the concepts of T-closed-coessential submodule and T-closed-coclosed submodule in the current study. More precisely, let Τ be a submodule of the R-module F and N, K are its submodules in which K ⊆ N, K is named as T-closed-co-essential (K≤Tc.ce N) of N in F if, N/K≪Tc T/K. Furthermore, N is called T-closed-coclosed (N≤Tc.cc F) if K≤Tc.ce N in F implies K=N. Several basic properties of these concepts have studies and proved. Moreover, many related examples have been presented in order to illustrate the mentioned concepts.

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