Strong lifting.

DOI10.1016/j.jalgebra.2004.11.019zbMath1132.16002OpenAlexW4213122181WikidataQ105369318 ScholiaQ105369318MaRDI QIDQ1772449

Yiqiang Zhou, W. Keith Nicholson

Publication date: 18 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.11.019

zbMATH Keywords

Jacobson radicalsoclesright idealssemiperfect ringssemiregular ringslifting idempotentsstrong liftingGoldie torsion ideal

Mathematics Subject Classification ID

Noncommutative local and semilocal rings, perfect rings (16L30) Ideals in associative algebras (16D25) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (34)

Annihilator-stability and unique generation ⋮ Corner Rings of a Clean Ring Need Not be Clean ⋮ On semiregular endomorphism rings and the dual of Yamagata's theorem ⋮ Comaximal factorization of lifting ideals ⋮ Unnamed Item ⋮ T-Semisimple Modules and T-Semisimple Rings ⋮ Semipotency and the total of rings and modules. ⋮ Unit lifting morphisms ⋮ Local \(I\)-semipotent rings ⋮ An Example of Bergman's and the Extension Problem for Clean Rings ⋮ Matrices having nonzero outer inverses ⋮ A CLASS OF EXCHANGE RINGS ⋮ Clean Index of Rings ⋮ SUBSTRUCTURES OF HOM ⋮ A generalization of projective covers ⋮ Generalizations of projectivity and supplements revisited for superfluous ideals ⋮ Two-sided properties of elements in exchange rings. ⋮ Rings with fine nilpotents ⋮ An ensemble of idempotent lifting hypotheses ⋮ Strong lifting splits. ⋮ Square-free modules with the exchange property. ⋮ A Generalization of Semiregular and Semiperfect Modules ⋮ Lifting properties of formal triangular matrix rings ⋮ Rings whose nonsingular modules have projective covers ⋮ A Generalization of Semiregular and Almost Principally Injective Rings ⋮ Half-orthogonal sets of idempotents ⋮ On (semi)regularity and the total of rings and modules. ⋮ Modules in Which Inverse Images of Some Submodules are Direct Summands ⋮ Unnamed Item ⋮ On weakly clean rings ⋮ Structural results on lifting, orthogonality and finiteness of idempotents ⋮ Exchange elements in rings, and the equation $XA-BX=I$ ⋮ Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical ⋮ Clean general rings.

Cites Work

• On pi-regular rings whose primitive factor rings are Artinian
• Extensions of exchange rings
• Semiregular, semiperfect and perfect rings relative to an ideal.
• Exchange property and the natural preorder between simple modules over semi-Artinian rings
• Raising idempotents
• WEAKLY CONTINUOUS AND C2-RINGS
• Semiregular Modules and Rings
• Lifting Idempotents and Exchange Rings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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