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Some results on ϕ-primary submodules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 12، دوره 16، شماره 10، دی 2025، صفحه 125-129 اصل مقاله (369.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33810.5051 | ||
| نویسندگان | ||
| Mohammad Hosein Moslemi Koopaei1؛ Masoud Zolfaghari* 2 | ||
| 1Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran | ||
| 2Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 03 اردیبهشت 1403، تاریخ پذیرش: 06 خرداد 1403 | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity, $M$ be an unitary $R$-module, let $\mathcal{S}(M)$ be the set of all submodules of $M$ and $\phi : \mathcal{S}(M)\rightarrow \mathcal{S}(M)\cup \lbrace\emptyset\rbrace$ be a function. A proper submodule $N$ of $M$ is called $\phi$-pimary submodule if $rx\in N \setminus \phi(N)$ where $r\in R$ and $x\in M$, implies that $x\in N$ or $r\in \sqrt{(N:M)}$. In this work, $\phi$-primary submodules are studied, and some results are obtained. | ||
| کلیدواژهها | ||
| ϕ-prime ideal؛ ϕ-primary ideal؛ ϕ-prime submodule؛ ϕ-primary submodule | ||
| مراجع | ||
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[1] D.D. Anderson and E. Batanieh, Generalizations of prime ideals, Commun. Algebra 36 (2008), 686–696. [2] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, 1969. [3] A. Barnard, Multiplication modules, J. Algebra 71 (1981), 174–178. [4] M. Ebrahimpour and F. Mirzaee, On ϕ-semiprime submodules, J. Korean Math. Soc. 54 (2017), no. 4, 1099–1108. [5] M. Ebrahimpour and R. Nekooei, On generalizations of prime submodules, Bull. Iran. Math. Soc. 39 (2013), no. 5, 919–939. [6] Z.A. El-Best and P.F. Smith. Multiplication modules, Comm. Algebra 16 (1998), no. 4, 755–779. [7] C.P. Lu, Prime submodules of modules, Commun. Math. Univ. Sancti Pauli 33 (1984), 61–69. [8] R.L. McCasland and M.E. Moore, Prime submodules, Commun. Algebra 20 (1992), 1803–1817. [9] R. Sharp, Steps in Commutative Algebra, Cambridge University Press, Cambridge, 2000. [10] N. Zamani, ϕ-prime submodules, Glasgow Math. J. 52 (2010), no. 2, 253–259. | ||
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