@article { author = {Ansari-Toroghy, Habibollah and Farshadifar, Faranak and Mahboobi-Abkenar, Farideh}, title = {The secondary radicals of submodules}, journal = {Algebraic Structures and Their Applications}, volume = {7}, number = {2}, pages = {1-13}, year = {2020}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2020.1786}, abstract = {Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual of primary radicals of submodules of $M$.}, keywords = {completely irreducible submodule,Secondary module,Secondary radical}, url = {https://as.yazd.ac.ir/article_1786.html}, eprint = {https://as.yazd.ac.ir/article_1786_ae582ddd64975ffedb22c5fc5d89f8bd.pdf} }