Characterizations of the commutators involving idempotents in certain subrings of $M_{2}(\mathbb{Z})$

DOI10.55730/1300-0098.3443OpenAlexW4385151356MaRDI QIDQ6176525

Tufan Özdin, Unnamed Author

Publication date: 25 July 2023

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

Full work available at URL: https://doi.org/10.55730/1300-0098.3443

zbMATH Keywords

idempotentcommutatornilpotentunit elementunit-regular elementclean (nil-clean) element

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Quadratic and bilinear Diophantine equations (11D09) Units, groups of units (associative rings and algebras) (16U60)

Cites Work

• Unnamed Item
• Weakly UU rings
• Rings of idempotent stable range one.
• Clean matrices and unit-regular matrices.
• Rings with internal cancellation.
• On idempotent stable range 1 matrices
• Nil clean rings.
• Properties of direct summands of modules
• Lifting Idempotents and Exchange Rings
• OnUJ-rings
• On rings with associated elements
• UNJ-Rings
• Rings such that, for each unit u, u − u n belongs to the Jacobson radical
• Nil-clean and unit-regular elements in certain subrings of ${\mathbb M}_2(\mathbb Z)$
• A nil-clean 2 × 2 matrix over the integers which is not clean

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