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Prime and primary submodules of certain modules

A. Amini, B. Amini, Habib Sharif (2006)

Czechoslovak Mathematical Journal

In this paper we characterize all prime and primary submodules of the free R -module R n for a principal ideal domain R and find the minimal primary decomposition of any submodule of R n . In the case n = 2 , we also determine the height of prime submodules.

Projective modules and prime submodules

Mustafa Alkan, Yücel Tiraş (2006)

Czechoslovak Mathematical Journal

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.

Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi (2003)

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of quasi-homeomorphisms, the Goldman prime spectrum and the Jacobson prime spectrum of a commutative ring. We prove that, if g : Y → X is a quasi-homeomorphism, Z a sober space and f : Y → Z a continuous map, then there exists a unique continuous map F : X → Z such that F ∘ g = f . Let X be a T 0 -space, q : X → s X the injection of X onto its sobrification X s . It is shown, here, that q ⁢ Gold ⁢ X = Gold ⁢ X s , where Gold ⁢ X is the set of all locally closed points of X . Some applications are also indicated. The Jacobson prime spectrum...

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