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On Almost $S$-prime submodules | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 27-42 اصل مقاله (343.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2022.22862.1427 | ||
| نویسندگان | ||
| F. Farzalipour* 1؛ R. Ghaseminejad2؛ M. S. Sayedsadeghi2 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with non-zero identity, $S\subseteq R$ be a multiplicatively closed subset of $R$ and let $M$ be an $R$-module. A submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be almost $S$-prime, if there exists an $s\in S$ such that whenever $rm\in N-(N:_{R}M)N$, then $sm\in N$ or $sr\in (N:_{R}M)$ for each $r\in R$, $m\in M$. The aim of this paper is to introduce and investigate some properties of the notion of almost $S$-prime submodules, especially in multiplication modules. Moreover, we investigate the behaviour of this structure under module homomorphisms, localizations, quotient modules, Cartesian product. Finally, we state two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are almost $S$-prime. | ||
| کلیدواژه‌ها | ||
| $S$-prime submodule؛ almost $S$-prime submodule؛ multiplication module | ||
| مراجع | ||
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1. M. M. Ali, Residual submodules of multiplication modules, Beit. Algebra Geom.,43 (2007), 321-343. 2. D. D. Anderson and M. Winders, Idealization of a module, Comm. Algebra, (1)1 (2009), 3-56. 3. H. Ansari Toroghi and S. S. Pourmortazavi, On S-primary submodules, Int.Electronic J. Algebra, 31 (2022), 74-89. 4. E. M. Bouba, N. Mahdou and M. Tamekkante, Duplication of a module along an ideal, Acta Math. Hungar, 154 (2018), 29-42. 5. M. D'Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl., 6 (2007), 443-459. 6. S. Ebrahimi Atani and F. Farzalipour, On weakly prime submodules, Tamkang J. of Math., (3) 28 (2007), 247-252. 7. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16 (1988), 755-779. 8. R. El Khalfaoui, N. Mahdou, P. Sahandi and N. Shirmohammadi, Amalgamated modules along an ideal, Comm. Korean Math. Soc., 36 (2021), 1-10. 9. F. Farzalipour, On almost semiprime submodules, Algebra, 2014 (2014), Article ID 752858, 6 pages. 10. F. Farzalipour and P. Ghiasvand, A generalization of graded prime submodules over non-commutative graded rings, J. Algebra Relat. Topics, (1) 8 (2020), 39-50. 11. F. Farzalipour and P. Ghiasvand, On S-1-absorbing prime submodules, J. Algebra Appl., (6) 21 (2022), 2250115, 14 pages. 12. H. A. Khashan, On almost prime submodules, Acta Mathematica Scientia, 32 (2012), 645-651. 13. A. Pekin, U. Tekir and O. Klc, S-semiprime submodules and S-reduced modules, J. Math., 2020 (2020), Article ID 8824787, 7 pages. 14. S. Rajaee, S-small and S-essential submodules, J. Algebra Relat. Topics, (1) 10 (2022), 1-10. 15. E. S. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turk. J. Math., (2) 43 (2019), 1036-1046. 16. G. Ulucak, U. Tekir and S. Koc, On S-2-absorbing submodules and vn-regular modules, An. St. Uni. Ovidius Constanta, (2) 28 (2020), 239-257. 17. F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Singapore: Springer, 2016. | ||
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