University of Guilan Journal of Algebra and Related Topics 2345-3931 2026 02 19 On characterization of $J_{\delta_{ss}}$-supplemented modules 9459 10.22124/jart.2026.30173.1784 EN E. Kaynar Vocational School of Technical Sciences‎, ‎Amasya University, Amasya‎, ‎Turkey.‎‎ Journal Article 2025 03 21 ‎Let an $S$-module $J$ be the ideal of $S$‎. ‎An $S$-module ‎$‎X‎$‎ is called $J_{\delta_{ss}}$-supplemented provided that there is a direct summand W of X with $X=Y+W$‎, ‎$Y\cap W\leq Soc_{\delta}(W)$ and $Y\cap W \subseteq WJ$ for each submodule $Y$ of a right module‎. ‎In this article‎, ‎the important features of this notion is presented‎, ‎its comparison with $\oplus_{ss}$-supplemented and $\delta{ss}$-supplemented modules is given‎. ‎$\oplus_{ss}$-supplemented modules $\delta_{ss}$-supplemented modules‎ Semisimple module‎ Semiperfect ring https://jart.guilan.ac.ir/article_9459_e80b0738fb29c718bda0e5a0e93ca591.pdf