Perspectivity and von Neumann regularity

DOI10.1080/00927872.2021.1948555zbMath1491.16005OpenAlexW3202999476MaRDI QIDQ5860717

Dinesh Khurana, Pace P. Nielsen

Publication date: 22 November 2021

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

Full work available at URL: https://doi.org/10.1080/00927872.2021.1948555

zbMATH Keywords

unit-regular elementsstrongly regular elementsvon Neumann regular elementsIC ringsspecial clean elementsperspective submodules

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Conditions on elements (16U99) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Idempotent elements (associative rings and algebras) (16U40)

Related Items (9)

An introduction to q-central idempotents and q-abelian rings ⋮ C4-modules with the exchange property ⋮ Perspectivity, exchange and summand-dual-square-free modules ⋮ Direct complements almost unique ⋮ Idempotent chains and bounded generation of \(\mathrm{SL}_2\) ⋮ Rings with transitive chaining of idempotents ⋮ On the structure of semigroups whose regular elements are completely regular ⋮ U-Modules with transitive perspectivity ⋮ N-chained semigroups and -perspective modules and rings

Cites Work

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• Exercises in classical ring theory.
• Rings with internal cancellation.
• Half-orthogonal sets of idempotents
• Idempotent lifting and ring extensions
• Units and One-Sided Units in Regular Rings
• Strongly clean rings and fitting's lemma
• Special clean elements in rings
• Weakly perspective rings and modules
• On internally cancellable rings

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