Stability of rings

zbMATH Open1199.20085arXiv1003.2301MaRDI QIDQ3553062

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Publication date: 22 April 2010

Abstract: The conditions for stability of the elements of linear groups over the associative rings with identity and their connection with the stability of rings are analyzed in the article. The stability of rings which are commutative, satisfy the conditions of stability of rank $geq2$, von Neumann regular, integer-algebraic, nearly local rings introduced by the author, is examined. The most important classical results of H. Bass, L. Vaserstein, S.H. Khlebutin, A.A. Suslin, J.S. Wilson, I.Z.Golubchik, are considered from the unified standpoint.

Full work available at URL: https://arxiv.org/abs/1003.2301

zbMATH Keywords

stabilityassociative ringslinear groups over rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Grothendieck groups, (K)-theory, etc. (16E20) Other matrix groups over rings (20H25) Algebraic systems of matrices (15A30) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Stability for linear groups (19B14)

Related Items (6)

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