A CLOSURE OPERATION IN RINGS

DOI10.1142/S0129167X01001039zbMath1083.16007OpenAlexW1991697156MaRDI QIDQ4807366

Pere Ara, Francesc Perera, Gert Kjaergård Pedersen

Publication date: 18 May 2003

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x01001039

zbMATH Keywords

Jacobson radicalexchange ringsvon Neumann regularityBass stable rankquasi-invertible elementsQB-ringsextremally rich \(C^*\)-algebrassemi-primitive rings

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Prime and semiprime associative rings (16N60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) General theory of (C^*)-algebras (46L05) Units, groups of units (associative rings and algebras) (16U60) Galois correspondences, closure operators (in relation to ordered sets) (06A15) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Stable range conditions (19B10)

Related Items (1)

On the algebraic closure in rings

Cites Work

• Bass's first stable range condition
• Advances in the theory of unitary rank and regular approximation
• Separative cancellation for projective modules over exchange rings
• An infinite analogue of rings with stable rank one
• Cancellation of projective modules over regular rings with comparability
• The stable range of \(C^*\)-algebras
• Local rings of exchange rings
• Lifting units modulo exchange ideals and C* -algebras with real rank zero

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