A Zariski Topology for Modules

DOI10.1080/00927872.2010.519748zbMath1253.16043arXiv1007.3149OpenAlexW2152005258MaRDI QIDQ2902259

Jawad Y. Abuhlail

Publication date: 17 August 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.3149

zbMATH Keywords

Zariski topologysober spacesHausdorff spacesduo modulesNoetherian spacescoatomic modulesirreducible spacesconnected spacesself-projective modulesFrechet spacesultraconnected spacesfully prime modulescomplete max-propertyS-PCD-modules

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Structure, classification theorems for modules and ideals in commutative rings (13C05) Other classes of modules and ideals in associative algebras (16D80) Topological fields, rings, etc. (topological aspects) (54H13) Topological and ordered rings and modules (16W80) Other special types of modules and ideals in commutative rings (13C13)

Related Items (9)

Zariski topology on the spectrum of fuzzy classical primary submodules ⋮ PS-hollow representations of modules over commutative rings ⋮ A generalization of quantales with applications to modules and rings. ⋮ Topological properties of the prime spectrum of a semimodule ⋮ Unnamed Item ⋮ ON THE NOTION OF STRONG IRREDUCIBILITY AND ITS DUAL ⋮ Zariski-like topologies for lattices with applications to modules over associative rings ⋮ Zariski Topologies for Coprime and Second Submodules ⋮ On S-Zariski topology

Cites Work

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• Coprime preradicals and modules.
• Fully coprime comodules and fully coprime corings.
• A note on indecomposable modules
• Pure submodules of direct products of free modules
• Koatomare Moduln
• An introduction to Zariski spaces over Zariski topologies
• Multiplication modules and projective modules
• Elementary properties of minimal and maximal points in Zariski spectra
• A Zariski topology for bicomodules and corings.
• Rings for which every cyclic module is quasi-projective
• Mean curvatures of a subspace in a Finsler space
• MODULES WITH COINDEPENDENT MAXIMAL SUBMODULES
• On the spectrum of a module over a commutative ring
• Some Remarks on Multiplication and Projective Modules
• DUO MODULES
• On Coprime Modules and Comodules
• THE LATTICE STRUCTURE OF PRERADICALS II: PARTITIONS
• Quasi-injective multiplication modules
• ASSOCIATED PRIMES OVER SKEW POLYNOMIAL RINGS
• Multiplication modules over non-commutative rings
• PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS
• Spectrum of a Noncommutative Ring
• On Prime Spectrums of Commutative Rings
• PRIME AND IRREDUCIBLE PRERADICALS

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