Special clean elements, perspective elements and perspective rings

DOI10.1142/S0219498823500901OpenAlexW4200442177MaRDI QIDQ5882590

Xavier Mary

Publication date: 17 March 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498823500901

zbMATH Keywords

unit-regular elementsstable range 1perspective rings(special) clean elements

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Conditions on elements (16U99) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Cites Work

• Perspective rings.
• Lower bounds on the stable range of polynomial rings
• A note on the group structure of unit regular ring elements
• Clean matrices and unit-regular matrices.
• Rings with internal cancellation.
• Classes of almost clean rings.
• Characterizations of clean elements by means of outer inverses in rings and applications
• Lifting Idempotents and Exchange Rings
• Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings
• Characterizations of special clean elements and applications
• Special clean elements in rings
• Uniquely Clean Elements in Rings