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http://dx.doi.org/10.5666/KMJ.2015.55.4.871

On Divisorial Submodules  

DARANI, AHMAD YOUSEFIAN (Department of Mathematics and Applications, University of Mohaghegh Ardabili)
RAHMATINIA, MAHDI (Department of Mathematics and Applications, University of Mohaghegh Ardabili)
Publication Information
Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 871-883 More about this Journal
Abstract
This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.
Keywords
divisorial submodule; prime submodule; radical submodule; multiplication module;
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1 M. M. Ali, Invertibility of multiplication modules, New Zealand J. Math., 35(2006), 17-29.
2 M. M. Ali, Invertibility of multiplication modules II, New Zealand J. Math., 39(2009), 45-64.
3 M. M. Ali, Some remarks on generalized GCD domains, Comm. Algebra, 36(2008), 142-164.   DOI
4 M. M. Ali, Invertibility of multiplication modules III, New Zealand J. Math., 39(2009), 139-213.   DOI
5 M. M. Ali, Idempotent and nilpotent submodules of multiplication modules, Comm. Algebra, 36(2008), 4620-4642.   DOI
6 M. M. Ali, The transform formula for submodules of multiplication modules, New Zealand J. Math., 41(2011), 25-37.
7 R. Ameri, On the prime submodules of multiplication modules, Internat. J. Math. Math. Sci., 27(2003), 1715-1724.
8 A. Barnard, Multiplication modules, J. Algebra, 71(1981), 174-178.   DOI
9 Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1998), 755-799.
10 E. Houston, S. Kabbaj, T. Lucas and A. Mimouni When is the dual of an ideal a ring?, J. Algebra, 225(2000), 429-450.   DOI
11 M. Fontana, J. Hukaba and I. Papick, Prufer Domains, Marcel Dekker, (1997).
12 R. Gilmer, Multiplicative ideal theory, Marcel Dekker: New York, (1972).
13 M. D. Larsen and P. J. MacCaarthy, Multiplication theory of ideal, Academic Press: New York, (1971).
14 A. G. Naoum, Flat modules and multiolication modules, Periodica. Math. Hungar., 21(1990), 309-317.   DOI
15 A. G. Naoum and F. H. Al-Alwan, Dedekind modules, Comm. Algebra, 24(1996), 225-230.
16 P. F. Smith, Multiplication modules, Comm. Algebra, 16(1988), 755-799.   DOI
17 P. F. Smith, Some remarks on multiplication modules, Arch. der. Math., 50(1988), 223-235.   DOI