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Shahabaddin Ebrahimi Atani (2004)
Czechoslovak Mathematical Journal
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First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
L. Bican, P. Jambor, Tomáš Kepka, P. Němec (1980)
Fundamenta Mathematicae
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Mustafa Alkan, Yücel Tiraş (2006)
Czechoslovak Mathematical Journal
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In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.
Atani, Shahabaddin Ebrahimi (2002)
International Journal of Mathematics and Mathematical Sciences
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Siamak Yassemi (2001)
Archivum Mathematicum
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In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.