Rings in which every prime ideal is contained in a unique maximal right ideal

DOI10.1016/0022-4049(92)90096-XzbMath0774.16001OpenAlexW1987699381MaRDI QIDQ1192258

Shu-Hao Sun

Publication date: 27 September 1992

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(92)90096-x

zbMATH Keywords

axiom of choiceGelfand dualitymaximal right idealsprime ideal theoremGelfand ringlattice of right idealsprime right idealsmaximal ideal theorem

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Prime and semiprime associative rings (16N60) Ideals in associative algebras (16D25)

Related Items (11)

Topologically boolean and g(x)-clean rings ⋮ Clean elements in Abelian rings. ⋮ Gelfand Factor Rings and Weak Zariski Topologies ⋮ A remark on Gelfand duality ⋮ Attaching topological spaces to a module. I: sobriety and spatiality ⋮ On semiabelian \(\pi\)-regular rings. ⋮ Noncommutative rings in which every prime ideal is contained in a unique maximal ideal ⋮ The ring of Colombeau’s full generalized quaternions ⋮ EXTENSIONS OF VON NEUMANN LOCAL RINGS ⋮ Spectrum of a Noncommutative Ring ⋮ Spectra of Maximal 1-Sided Ideals and Primitive Ideals

Cites Work

• Unnamed Item
• Algebra in a localic topos with applications to ring theory
• Erratum to: Reticulated rings
• A generalisation of Gel'fand duality
• Noncommutative rings in which every prime ideal is contained in a unique maximal ideal
• On separation lemmas
• A Sheaf Representation for Modules with Applications to Gelfand Rings
• Commutative Rings in Which Every Prime Ideal is Contained in a Unique Maximal Ideal

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