Upper complete intersection dimension relative to a local homomorphism
Recently many authors studied new homological invariants: complete intersection dimension, Gorenstein dimension and others. They have similar properties as projective dimension. In the present paper, the author adds one more new invariant, called upper complete intersection dimension relative to a local homomorphism, to the sequence of homological invariants above. Let \(R\) be a Noetherian local ring and \(M\) a finitely generated \(R\)-module. The complete intersection dimension and others are integers (or symbol \(\infty\)) assigned to~\(M\). However, the relative upper complete intersection dimension is assigned to the pair of~\(M\) and a local homomorphism \(\phi \: S \to R\), where \(S\) is another Noetherian local ring. It properly depends on the choice of~\(\phi\). It is possible that the relative upper complete intersection dimension has more information of~\(M\) than other homological dimensions.
scientific article; zbMATH DE number 2124829