Cofinitely $\bigoplus D_j$-supplemented modules

Document Type : Research Paper


Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq


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.


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Volume 13, Issue 2
July 2022
Pages 2399-2403
  • Receive Date: 14 January 2022
  • Revise Date: 04 March 2022
  • Accept Date: 18 April 2022