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Weakly semi-primary submodules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 18، دوره 13، شماره 2، مهر 2022، صفحه 185-190 اصل مقاله (348.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6235 | ||
| نویسندگان | ||
| Mamoon F. Khalf* 1؛ Obaida Amer Radhi2 | ||
| 1Department of Physics, College of Education, University of Samarra, Iraq | ||
| 2Department of Education Al-Dur, General Directorate of Education for Salah Al-Din, Ministry of Education, Iraq | ||
| تاریخ دریافت: 21 آذر 1400، تاریخ بازنگری: 28 دی 1400، تاریخ پذیرش: 20 بهمن 1400 | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity, and let $W$ be a unitary $R$-module. In this paper, we introduced the concept of a weakly semi-primary submodule as a generalization of the primary submodule, where a submodule $X$ of $W$ is called weakly semi-primary if the \(\mathrm{Rad}(X:W) = \sqrt{(X:W)}\) is a weakly prime ideal of $R$, and from this work, we have provided some characteristics of weakly semi-primary submodule. | ||
| کلیدواژهها | ||
| Weakly semi-primary؛ weakly prime؛ multiplication module؛ Weakly semi-primary ring؛ local ring and finitely generated | ||
| مراجع | ||
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[1] D.D. Anderson and E. Smith, Weakly prime ideals, Huston J. Math. 29 (2003), no. 4, 831–840. [2] A. Barnard, Multiplication modules, J. Alg. 71 (1981), 174–178. [3] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, 1956. [4] Z.A. El-Bast and P.F. Smith, Multiplication modules, Comm. Alg. 16 (1988), 755–779. [5] R.W. Gilmer, Ring in which semi-primary ideal are primary, Pac. J. Math. 12 (1962), 1273–1276. [6] M.D. Larsen and P.J. McCarthy, Multiplicative theory of ideals, Academic press, New York and London, 1971. [7] A.S. Mijbass, On cancellation modules, M. Sc. Thesis, University of Baghdad, 1992. [8] H. Prufer, Untersuchungen uber teilbarkeitsenschaften in korpern, J. Reine Angew. Math. 168 (1932), 1–36. [9] S.A. Saymeh, On prime R-submodules, Univ. Nac. Tucuman Rev. Ser. A 29 (1979), no.1, 121–136. [10] O. Zariski and P. Samuel, Commutative algebra, Vol.I, D. Van Nostrand Company, Inc., 195 | ||
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