Some results of multiplication modules. (English) Zbl 1504.13018
Summary: In this paper, we state a number of results about associated and supported prime ideals and prime submodules, respectively, and then we study these results about multiplication and weakly finitely generated \(R\)-modules in some cases. Finally, after recalling the definition of a complement to a submodule in a module, we find some properties of associated and supported prime submodules of a module in connection with complement.
MSC:
| 13E05 | Commutative Noetherian rings and modules |
| 13E10 | Commutative Artinian rings and modules, finite-dimensional algebras |
| 13C99 | Theory of modules and ideals in commutative rings |
References:
| [1] | R. B. Ash, A Course in Commutative Algebra, www. math.uiuc.edu/r-ash@copyright (2003). |
| [2] | Barnard, A., Multiplication modules, J. Algebra71 (1981) 174-178. · Zbl 0468.13011 |
| [3] | EL-Bast, Z. A. and Smith, P. F., Multiplication modules, Comm. Algebra16(4) (1988) 755-779. · Zbl 0642.13002 |
| [4] | Lu, C. P., Prime submodules of modules, Comment. Math. Univ. St. Paul.33(1) (1984) 61-96. · Zbl 0575.13005 |
| [5] | Matsumura, H., Commutative Algebra (Benjamin/Cumming Publishing Company, Reading, M. A., 1980). · Zbl 0441.13001 |
| [6] | McCasland, R. L. and Smith, P. F., Prime submodules of Noetherian modules, Rocky Mountain J. Math.23(3) (1993) 1041-1062. · Zbl 0814.16017 |
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