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Notes on reduced, artinian and multiplication modules | ||
| Journal of Hyperstructures | ||
| دوره 3، شماره 2، اسفند 2014، صفحه 108-115 اصل مقاله (99.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2014.2582 | ||
| نویسندگان | ||
| Jafar A’zami* 1؛ Mahdieh Savaedi2 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabil, Iran. | ||
| 2Department of Mathematics, Sosangerd Branch, Islamic Azad University , Sosangerd, Iran. | ||
| چکیده | ||
| Let M be a unitary module over a commutative ring R with identity. In this paper we consider the concepts of Artinian, semi-Artinian, reduced and multiplication modules . Also we call an R-module M radical, if it has no maximal submodule. By P(M) we denote the sum of the radical submodules of M and we show that P(M/(P(M)) = 0. | ||
| کلیدواژهها | ||
| Artinian modules؛ Associated primes؛ Semi-Artinian modules؛ Multiplication modules؛ Reduced modules | ||
| مراجع | ||
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[1] Bruns, W. and Herzog, J., Cohen Macualay rings, Cambridgestudies in advanced mathematics, (1997). [2] El-Bast, Z. A. and Smith, P. F., Multiplication modules, Comm. in Algebra, 16(1988), 755-779. [3] Matsumura, H., Commutative ring theory, Cambridge Univ. Press, Cambridge, UK, 1986. [4] Rudlof, P., On minimax and related modules, Can. J. Math. Vol. 44(1),(1992),154-166. [5] Sharpe, D. W. and Vamos, P., Injective modules, (Lectures in pure Mathematics), University of sheffield, (1972). | ||
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