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On primary isolated submodules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 131، دوره 13، شماره 1، خرداد 2022، صفحه 1605-1611 اصل مقاله (369.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5775 | ||
| نویسندگان | ||
| Ghaleb Ahmed* ؛ Tamara Alshareef | ||
| Department of Mathematics, College of Education for Pure Science, Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq | ||
| تاریخ دریافت: 11 آبان 1400، تاریخ پذیرش: 09 آذر 1400 | ||
| چکیده | ||
| Let \(L\) be a left module over a ring \(\text{\ S}\) with identity. In this paper, the concept of primary isolated submodules is introduced. We look for relations between this class of submodules and related modules. A number of facts and characterizations that concern is gained. The aim of this work is to introduce and study the primary isolated submodules as a generalization of isolated submodules. A submodule \(A\) of \(L\) is primary isolated if for each proper \(B\) of \(A\), there is a primary submodule \(C\) of \(L\), \(B \subseteq C\) but\(\text{\ A} \nsubseteq C\). Some properties are gained and we look for any relationship between this type of modules and other related modules. | ||
| کلیدواژه‌ها | ||
| Primary isolated submodules؛ Primary lifted submodules؛ Primary radical submodules؛ Primary submodules؛ Prime submodules | ||
| مراجع | ||
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[1] G. Ahmed, Some Generalization of Regular Modules, Ph. D. Thesis, College of Science, University of Baghdad, 2015. [2] G. Ahmed, The primary radical of submodules, Iraqi J. Sci. to appear. [3] R.L. McCasland and P.F. Smith, On isolated submodules, Commut. Alge. 34(8) (2006) 2977–2988. [4] P.F. Smith, Primary modules over commutative rings, Glasgow Math. J. 43(1) (2001) 103–111. [5] R. Wisbauer, Foundations of Modules and Rings Theory, Philadelphia, Gordon and Breach, 1991. [6] S.M. Yaseen, F-Regular Modules, M.Sc. Thesis, College of Science, University of Baghdad, 1993. | ||
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