On finitely generated projective ideals and Ohm condition
type: Item
instance of: scholarly article
title: On finitely generated projective ideals and Ohm condition
zbMATH Open document ID: 0579.13006
DOI: 10.1007/BF01855803
author: Adil G. Naoum
author: Mohammed A. Hasan
published in: Periodica Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: For a commutative ring R with an identity, a row n vector \(U\in R^ n\) is semiregular if an \(n\times n\) matrix M over R exists such that \(UM=U\) and \(ann(U)=ann(M)\) where \(ann(U)=\{x\in R^ n| xU^ t=0\}\) and ann(M) is defined similarly. M is ''associated with the n-vector U''. Some properties of matrices associated to semiregular vectors are studied. Later on it is proved that the product of a finite number of finitely generated projective ideals (a finitely generated ideal \(I=id(a_ 1,...,a_ n)\) is projective iff the vector \((a_ 1,a_ 2,...,a_ n)\) is semiregular) is again projective. - Later on Ohm type properties for finitely generated projective ideals are studied.
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 3927056
zbMATH Keywords: projective ideals
zbMATH Keywords: Ohm condition
zbMATH Keywords: matrices associated to semiregular vectors
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3927056