TY - JOUR T1 - On S-primary submodules AU - Ansarı-toroghy, H. AU - Pourmortazavi, S. S. PY - 2022 DA - January DO - 10.24330/ieja.1058417 JF - International Electronic Journal of Algebra JO - IEJA PB - Abdullah HARMANCI WT - DergiPark SN - 1306-6048 SP - 74 EP - 89 VL - 31 IS - 31 LA - en AB - Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module. In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is shown that this class of modules contains the family of primary (resp. $S$-prime) submodules properly. KW - Multiplicatively closed subset KW - prime submodule KW - $S$-prime submodule KW - primary submodule KW - $S$-primary submodule CR - R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715-1724. CR - D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56. CR - J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181. CR - Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779. CR - F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404. CR - R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, 1992. CR - C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33(1) (2007), 125-143. CR - R. L. McCasland and M. E. Moore, On radicals of submodules of finitely generated modules, Canad. Math. Bull., 29(1) (1986), 37-39. CR - R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803-1817. CR - M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, 1962. CR - E. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turkish J. Math., 43(2) (2019), 1036-1046. CR - F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016. UR - https://doi.org/10.24330/ieja.1058417 L1 - https://dergipark.org.tr/en/download/article-file/2194481 ER -