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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.