Semihereditary semichain rings
type: Item
instance of: scholarly article
title: Semihereditary semichain rings
zbMATH Open document ID: 0631.16008
DOI: 10.1007/BF01057491
author: O. E. Gregul'
author: V. V. Kirichenko
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The authors prove that any semichain semihereditary ring A is equivalent to a direct product of cell-triangular matrix rings \[ k= \begin{pmatrix} A_ 1 & M_{n_ 1 \times n_ 2}(D) & ... & M_{n_ 1 \times n_ t}(D) \\ 0 & A_ 2 & ... & M_{n_ 2 \times n_ t}(D) \\ 0 & 0 & ... & ... \\ 0 & 0 & 0 & A_ t \end{pmatrix} \] in the sense of Morita contexts. Rings \(A_ 1,...,A_ t\) are prime, semichain and semihereditary. The ring of quotients \(\tilde A_ i\) for \(A_ i\) is isomorphic to some matrix ring \(M_{n_ i}(D)\), \(i=1,...,t\) over a skew field D. Proving this theorem the authors use two helpful results: (i) any semiprime semichain ring is a direct product of prime rings; (ii) any semichain ring has a classical ring of quotients.
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16P50
zbMATH DE Number: 4025634
zbMATH Keywords: direct product of cell-triangular matrix rings
zbMATH Keywords: semiprime semichain ring
zbMATH Keywords: direct product of prime rings
zbMATH Keywords: classical ring of quotients
reviewed by: L.Sh.Ioffe
MaRDI profile type: Publication
cites work: Q5637025
cites work: Piecewise domains
cites work: Torsion-free modules and rings
full work available at URL: https://doi.org/10.1007/bf01057491
OpenAlex ID: W2019253339
description: scientific article; zbMATH DE number 4025634