Rings without infinite sets of noncentral orthogonal idempotents.

DOI10.1007/S10958-009-9656-ZzbMath1205.16003OpenAlexW2042565241MaRDI QIDQ844553

Askar A. Tuganbaev

Publication date: 19 January 2010

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9656-z

zbMATH Keywords

right semi-Artinian ringsexchange ringsPierce stalkssemiperfect rings\(I_0\)-modulesArtinian serial ringsorthogonal idempotents

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Noncommutative local and semilocal rings, perfect rings (16L30) Conditions on elements (16U99) Other classes of modules and ideals in associative algebras (16D80) Artinian rings and modules (associative rings and algebras) (16P20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (7)

Abelian groups with nilpotent commutators of endomorphisms. ⋮ Fully idempotent homomorphisms. ⋮ \(I_0^*\)-modules ⋮ Homogeneous maps of Abelian groups. ⋮ Generalized SV-rings of bounded index of nilpotency. ⋮ Regular semi-Artinian rings. ⋮ Completely decomposable Abelian groups with clean endomorphism rings.

Cites Work

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• Semiregular, weakly regular, and \(\pi\)-regular rings
• Exchange property and the natural preorder between simple modules over semi-Artinian rings
• \(I\)-like modules
• Closure of weakly regular modules with respect to direct sums.
• Weakly regular modules.
• I-Rings
• Pierce sheaves of non-commutative rings
• Lifting Idempotents and Exchange Rings
• Exchange rings, units and idempotents

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