The aim of this article is to investigate a new class of ideals called soc-ideals, which constitute a subclass of r-ideals introduced in Mohamadian, R., Turk. J. Math. 39(5), 733–749 (2015). Let R be a commutative ring. A proper ideal \(\mathfrak {p}\) of R is said to be a soc-ideal of R, if whenever \(a,b\in R\) such that \(ab\in \mathfrak {p}\) , then \(a\in \mathfrak {p}\) or \(b\in \text {Soc}(R)\) . We prove several results, properties, and examples regarding soc-ideals. In particular, we investigate rings which admit soc-ideals, rings in which all ideals are soc-ideals, and rings in which r-ideals and soc-ideals coincide. Moreover, we use these findings to characterize non semisimple rings in which all ideals are weakly prime in terms of soc-ideals. Finally, the article investigates the socle of some rings such as Nagata’s idealization of modules \(R\propto M\) and the amalgamation duplication of rings \(R\bowtie ^{\rho }\mathfrak {q}\) . Based on these findings, we give original characterizations of soc-ideals in these types of rings. Two new properties of the ring \(R\propto M\) are concluded from our study of soc-ideals.
