Euclidean pairs and quasi-Euclidean rings.

DOI10.1016/j.jalgebra.2014.02.009zbMath1318.16036OpenAlexW2080780011MaRDI QIDQ402430

André Leroy, Adel N. Alahmadi, Surender Kumar Jain, Tsit-Yuen Lam

Publication date: 28 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.02.009

zbMATH Keywords

Bézout ringsvon Neumann regular ringsidempotent matricesunit-regular ringsGE-ringsHermite ringsnoncommutative Euclidean ringsquasi-Euclidean rings

Mathematics Subject Classification ID

Factorization of matrices (15A23) Endomorphism rings; matrix rings (16S50) Generalizations of commutativity (associative rings and algebras) (16U80) Algebraic systems of matrices (15A30) Divisibility, noncommutative UFDs (16U30) Euclidean rings and generalizations (13F07) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (15)

On some Euclidean properties of matrix algebras ⋮ Elementary matrices and products of idempotents ⋮ Idempotent factorizations of singular 2 × 2 matrices over quadratic integer rings ⋮ Reverse decomposition of unipotents over noncommutative rings. I: General linear groups ⋮ When are nonnegative matrices product of nonnegative idempotent matrices? ⋮ On finitely generated modules over quasi-Euclidean rings ⋮ Leapfrog constructions: from continuant polynomials to permanents of matrices ⋮ On quotients of generalized Euclidean group rings ⋮ Quasi-permutation singular matrices are products of idempotents ⋮ Decomposition of singular elements of an algebra into product of idempotents, a survey ⋮ Singular matrices that are products of two idempotents or products of two nilpotents ⋮ Factorizations into idempotent factors of matrices over Prüfer domains ⋮ Equivalent generating vectors of finitely generated modules over commutative rings ⋮ Presentations for singular wreath products ⋮ 𝑈-rings generated by its idempotents

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