Products of idempotents in regular rings. II

DOI10.1016/0021-8693(89)90044-6zbMath0673.16007OpenAlexW2094597643MaRDI QIDQ1120643

John Hannah, K. C. O'Meara

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90044-6

zbMATH Keywords

direct sumsrank functionsannihilatorsidempotent matricesproducts of idempotentsunit-regular ringdirectly finite simple regular ringsweak-unit-regularity

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Conditions on elements (16U99) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (25)

On n-generalized commutators and Lie ideals of rings ⋮ Elementary matrices and products of idempotents ⋮ Products of idempotent integer matrices ⋮ Idempotent factorizations of singular 2 × 2 matrices over quadratic integer rings ⋮ Regular bisimple rings ⋮ Cancellation of projective modules over regular rings with comparability ⋮ Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings ⋮ Another multiplicative property of a regular ring that has no multiplicative proof ⋮ Simple regular rings satisfying weak comparability ⋮ When are nonnegative matrices product of nonnegative idempotent matrices? ⋮ Decomposition of singular matrices into idempotents ⋮ On Generalized Stable Ideals ⋮ On generalized stable rings ⋮ Modules that are invariant with respect to automorphisms and idempotent endomorphisms of their hulls and covers ⋮ Quasi-permutation singular matrices are products of idempotents ⋮ Decomposition of singular elements of an algebra into product of idempotents, a survey ⋮ Idempotents in triangular matrix rings ⋮ Separative cancellation for projective modules over exchange rings ⋮ Products of simultaneously triangulable idempotent matrices ⋮ Factorizations into idempotent factors of matrices over Prüfer domains ⋮ 𝑈-rings generated by its idempotents ⋮ Modules which are invariant under nilpotents of their envelopes and covers ⋮ On rings whose nonunits are a unit multiple of a nilpotent ⋮ Products of idempotents in separative regular rings ⋮ A new setting for constructing von Neumann regular rings

Cites Work

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• The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space
• Products of idempotent linear transformations
• Products of idempotents in regular rings
• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup
• On products of idempotent matrices
• Products of idempotent matrices

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