Zariski spaces of modules

Nikseresht, Ashkan; Azizi, A.

doi:10.1016/j.jpaa.2012.10.014

Journal of Pure and Applied Algebra

2013

DOI: 10.1016/j.jpaa.2012.10.014

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Zariski spaces of modules

Ashkan Nikseresht

A. Azizi

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Cited by 2 publications

References 7 publications

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Semi-irreducible Zariski spaces of modules

Nikseresht

Azizi

2014

J. Algebra Appl.

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In this paper, we state conditions under which, the family of semi-irreducible submodules of a module determine a Zariski space of that module and study the properties of this space. Also we characterize semi-irreducible submodules of finitely generated modules over Dedekind domains. Moreover, assuming that M and M′ are finitely generated modules over a Dedekind domain having isomorphic semi-irreducible Zariski spaces, we find some common properties of M and M′. In particular, we show that in this case the torsion-free components of M and M′ have the same rank and the torsion submodules of [Formula: see text] and [Formula: see text] are isomorphic, where N and N′ are the intersection of all semi-irreducible submodules of M and M′, respectively.

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Semi-irreducible Zariski spaces of modules

Nikseresht

Azizi

2014

J. Algebra Appl.

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On topological lattices and their applications to module theory

Abuhlail

Lomp

2016

J. Algebra Appl.

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Abstract. We introduce the notion of a (strongly) topological lattice L = (L, ∧, ∨) with respect to a subset X L; a prototype is the lattice of (two-sided) ideals of a ring R, which is (strongly) topological with respect to the prime spectrum of R. We investigate and characterize (strongly) topological lattices. Given a non-zero left R-module M, we introduce and investigate the spectrum Spec f (M ) of first submodules of M. We topologize Spec f (M ) and investigate the algebraic properties of R M by passing to the topological properties of the associated space.

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Zariski spaces of modules

Cited by 2 publications

References 7 publications

Semi-irreducible Zariski spaces of modules

Semi-irreducible Zariski spaces of modules

On topological lattices and their applications to module theory

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