Some abstract maximal ideal-like spaces

DOI10.1007/BF01243875zbMath0685.06003MaRDI QIDQ1825889

Ioana Voiculescu, George Georgescu

Publication date: 1989

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

zbMATH Keywords

distributive latticesmaximal ideal spacecommutative ringssheaf representationsradical elementsframe of open setsintegral complete lattice-ordered groupoidsmultiplicative ideal structuresspatial frame of idealsvirginal elements

Mathematics Subject Classification ID

Structure and representation theory of distributive lattices (06D05) Lattice ideals, congruence relations (06B10) Subalgebras, congruence relations (08A30) Ideals and multiplicative ideal theory in commutative rings (13A15) Ordered semigroups and monoids (06F05) Continuous lattices and posets, applications (06B35)

Related Items (10)

Boolean lifting property in quantales ⋮ Rings and sheaves ⋮ Reticulation of a quantale, pure elements and new transfer properties ⋮ Compact representations - the lattice theory of compact ringed spaces ⋮ On separation lemmas ⋮ Flat topology on the spectra of quantales ⋮ Representations of MV-algebras by sheaves ⋮ Rickart residuated lattices ⋮ Spectra of monoidal-lattices ⋮ Sheaf representations of BL-algebras

Cites Work

• Isomorphic sheaf representations of normal lattices
• Reticulated rings
• A generalisation of Gel'fand duality
• On a representation of a strongly harmonic ring by sheaves
• A Sheaf Representation for Modules with Applications to Gelfand Rings
• Sheaf representations of strongly harmonic rings
• Lattice Aspects of Radical Ideals and Choice Principles
• Global subdirect products
• Representation of Universal Algebras by Sheaves
• A unified theory of minimal prime ideals
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