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Cofinitely $\bigoplus D_j$-supplemented modules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 193، دوره 13، شماره 2، مهر 2022، صفحه 2399-2403 اصل مقاله (377.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6566 | ||
| نویسندگان | ||
| Amenah Hasan* ؛ Wasan Khalid | ||
| Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq | ||
| تاریخ دریافت: 24 دی 1400، تاریخ بازنگری: 13 اسفند 1400، تاریخ پذیرش: 29 فروردین 1401 | ||
| چکیده | ||
| For any $R$-module $W,\ D_j(W)$ presented as the total of all $J$-small sub-modules. If $A$ and $B$ are sub-module of $W$, we say $A$ is $\bigoplus \ D_j$'supplement of $B$ in $W$ if $W=A+B=A\bigoplus \acute{A}$, for $\acute{A}\underline{\hookrightarrow}W$, and $A\bigcap B\ll_j D_j(A)$. If every sub-module has $\bigoplus \ D_j$-supplemented, then $W$ is $\bigoplus \ D_j$-supplemented $A$ sub-module $A$ of $W$. If a sentence is conclusive, it is said to be cofinite i.e., $\frac{W}{A}$ is finitely generated. Also we introduce cofinite $\bigoplus \ D_j$-supplemented if every cofinite sub-module of $W$ has $\bigoplus \ D_j$-supplemented. | ||
| کلیدواژهها | ||
| Cofinite؛ finitely generated؛ module؛ supplemented module | ||
| مراجع | ||
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[1] J.L. Garcia, Properties of direct summands of modules, Commun. Algebra 17 (1989), no. 1, 73–92. [2] A. Haramanci, D. Keskin and P.F. Smith, On L-supplemented Modules, Acta Math. Hungar. 83 (1999), no. 1, 161–169. [3] A.A. Hussein and W. Khalid, L−RadJ-supplemented modules, J. Phys.: Conf. Ser. IOP Publishing, 1818 (2021), no. 1, p. 012203. [4] A. Kabban and W. Khalid, On Jacobson-small sub-modules, Iraqi J. Sci. 60 (2019), no. 7, 1584–1591. [5] F. Kasch, Modules and rings, Academic press, 1982. [6] M.T. Ko¸san, Generalized cofinitely semiperfect modules, Int. Electr. J. Algebra 5 (2009), no. 5, 58–69. [7] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Philadelphia, 1991. | ||
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