Cristodor Ionescu
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View article: About the Cohen-Macaulay defect and almost Cohen-Macaulay rings
About the Cohen-Macaulay defect and almost Cohen-Macaulay rings Open
We notice the connection between almost Cohen-Macaulay rings and the Cohen-Macaulay defect. We introduce a Serre-type condition for modules, that is connected to the Cohen-Macaulay defect in the same way that the condition $(S_n)$ is conne…
View article: A locally F-finite Noetherian domain that is not F-finite
A locally F-finite Noetherian domain that is not F-finite Open
Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.
View article: Finite generation of André–Quillen (co-)homology of F-finite algebras
Finite generation of André–Quillen (co-)homology of F-finite algebras Open
We prove that the Andre-Quillen homology and cohomology modules of F-finite Z(p)-algebras are finitely generated.
View article: A locally F-finite Noetherian domain that is not F-finite
A locally F-finite Noetherian domain that is not F-finite Open
Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.
View article: Tensor products and direct limits of almost Cohen-Macaulay modules
Tensor products and direct limits of almost Cohen-Macaulay modules Open
We investigate the almost Cohen-Macaulay property and the Serre-type condition $(C_n),\ n\in\mathbb{N},$ for noetherian algebras and modules. More precisely, we find permanence properties of these conditions with respect to tensor products…
View article: Flat local morphisms of rings with prescribed depth and dimension
Flat local morphisms of rings with prescribed depth and dimension Open
For any pairs of integers (n,m) and (d, e) such that 0 ≤ n ≤ m, 0 ≤ d _ e, d ≤ n, e ≤ m and n -d ≤ m - e we construct a local flat ring morphism of noetherian local rings u : A → B such that dim(A) = n; depth(A) = d; dim(B) = m and depth(B…
View article: More properties of almost Cohen-Macaulay rings
More properties of almost Cohen-Macaulay rings Open
Some interesting properties of almost Cohen-Macaulay rings are investigated, and a Serre type property connected with this class of rings is studied.