Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology groups assumed to vanish may be arbitrarily far apart

Part 1 of this project is concerned with proving a relative version of the results in [1]. Consider the category of Lefschetz rings in which the objects are rings of equal characteristic zero which are realized as an ultraproduct of Noetherian rings of positive characteristic, and the morphisms between two such ultraproducts are given as ultraproducts of homomorphisms between the components. A ...

We consider random hermitian matrices in which distant abovediagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has algebraic Stieltjes transform by an argument based on dimension theory of noetherian local rings.

1.1 Statement (Matijevic–Roberts type theorem (MRTT)). Let C be a class of noetherian local rings. Let R be a noetherian Z-graded ring, and P its prime ideal. Let P ∗ be the prime ideal generated by the all homogeneous elements of P . If RP ∗ ∈ C, then RP ∈ C. Clearly, the truth of the statement depends on the choice of C. Nagata conjectured the Matijevic–Roberts type theorem for the case that ...

Let $G$ be an abelian group and $S$ a given multiplicatively closed subset of commutative $G$-graded ring $A$ consisting homogeneous elements. In this paper, we introduce study $S$-Noetherian modules which are generalization modules. We characterize in terms For instance, $A$-module $M$ is if only $S$-Noetherian, provided finitely generated countable. Also, generalize some results on Noetherian...

We study certain properties of Noetherian rings with weak normality and seminormality in mixed characteristic. It is known that the two concepts can differ equal prime characteristic case, while they coincide by definition zero case. exhibit some examples also establish local Bertini theorem for under a condition.

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using t...

Let R <-* S be an embedding of associative noetherian rings such that 5 is finitely generated as a right Ä-module. There is a correspondence from the prime spectrum of S to the prime spectrum of R obtained by associating to a given prime ideal P of S the prime ideals of R minimal over P n R . The prime and primitive ideal theories for several specific noncommutative noetherian rings, including ...

We show that some basic results on the K–theory of noetherian rings can be extended to coherent rings.