Exchange elements in rings, and the equation $XA-BX=I$

DOI10.1090/tran6652zbMath1396.16033OpenAlexW2395340538MaRDI QIDQ2826768

Dinesh Khurana, Pace P. Nielsen, Tsit-Yuen Lam

Publication date: 18 October 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran6652

zbMATH Keywords

idempotentsregular elementsclean elementsexchange elementssuitable elementssuitable ringslinear and quadratic equations

Mathematics Subject Classification ID

Conditions on elements (16U99)

Related Items (10)

Suitable elements, -clean elements and Sylvester equations in rings with involution ⋮ Strong exchange rings ⋮ Special clean elements in rings ⋮ Weak inverses of products — Cline’s formula meets Jacobson lemma ⋮ Two-sided properties of elements in exchange rings. ⋮ An ensemble of idempotent lifting hypotheses ⋮ Clear rings and clear elements ⋮ On cleanness of von Neumann algebras ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• Two-sided properties of elements in exchange rings.
• Algebras over zero-dimensional rings
• Separative cancellation for projective modules over exchange rings
• Clean matrices and unit-regular matrices.
• Strong lifting.
• Nil clean rings.
• Exchange rings and decompositions of modules
• EXTENSIONS OF CLEAN RINGS
• Corner Rings of a Clean Ring Need Not be Clean
• A CLASS OF EXCHANGE RINGS
• Lifting Idempotents and Exchange Rings
• Unit regular elements in corner rings
• Strongly clean rings and fitting's lemma
• On exchange rings
• Clean Index of Rings
• A Question on Strongly Clean Rings
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• A Characterization of Exchange Rings

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