On finitely generated projective ideals and Ohm condition
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.
matrices associated to semiregular vectors
scientific article; zbMATH DE number 3927056