Clear rings and clear elements

DOI10.30970/ms.55.1.3-9zbMath1473.16031OpenAlexW3133521623MaRDI QIDQ2028176

O. M. Romaniv, O. V. Domsha, B. V. Zabavs'kyj

Publication date: 31 May 2021

Published in: Matematychni Studiï (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.30970/ms.55.1.3-9

zbMATH Keywords

Bézout domainelementary divisor ringfull matrixclean elementclear elementclear ringunit-regular element

Mathematics Subject Classification ID

Conditions on elements (16U99) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Stable range conditions (19B10) Arithmetic rings and other special commutative rings (13F99)

Related Items (2)

Note on clear rings ⋮ Unnamed Item

Cites Work

• Algebras over zero-dimensional rings
• Clean matrices and unit-regular matrices.
• Two classes of rings generated by their units
• Exchange rings and decompositions of modules
• On a class of regular rings that are elementary divisor rings
• Exchange elements in rings, and the equation $XA-BX=I$
• 2-GOOD RINGS
• 2-Clean Rings
• Units and One-Sided Units in Regular Rings
• Lifting Idempotents and Exchange Rings
• Exchange rings, units and idempotents
• Conditions for stable range of an elementary divisor rings
• An Ideal-Theoretic Characterization of the Ring of All Linear Transformations
• Every Linear Transformation is a Sum of Nonsingular Ones
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