相关论文: Dimension theory in iterated local skew power seri…

We study skew inverse power series extensions R[[y^{-1};tau,delta]], where R is a noetherian ring equipped with an automorphism tau and a tau-derivation delta. We find that these extensions share many of the well known features of…

The global dimension of a ring governs many useful abilities. For example, it is semi-simple if the global dimension is 0, hereditary if it is 1 and so on. We will calculate the global dimension of a Crystalline Graded Ring, as defined in…

The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second subject consists of investigating the class of S-modules…

We introduce a naive notion of a system of parameters for a homologically finite complex over a commutative noetherian local ring, and compare it to the system of parameters defined by Christensen. We show that these notions differ in…

Given an iterated skew polynomial ring C[y_1;t_1,d_1]ldots [y_n;t_n,d_n] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m + < y_1,y_2,ldots,y_n> is an iterated skew…

In 2007, Y. Shimoda, in connection with a long-standing question of J. Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most…

In this paper, we investigate the structure of skew power series rings of the form $S = R[[x;\sigma,\delta]]$, where $R$ is a complete filtered ring and $(\sigma,\delta)$ is a skew derivation respecting the filtration. Our main focus is on…

We define and study two generalizations of the Krull dimension for rings, which can assume cardinal number values of arbitrary size. The first, which we call the "cardinal Krull dimension," is the supremum of the cardinalities of chains of…

Two are the objectives of the present paper. First we study properties of a differentially simple commutative ring R with respect to a set D of derivations of R. Among the others we investigate the relation between the D-simplicity of R and…

Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…

We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension two, we provide answers to some problems raised by Smirnov, and give a criterion to answer one of his questions in terms of a…

A power series ring over non-Noetherian rings can fail to be flat over the base ring, and its dimension can be infinite, even when the dimension of the base ring is finite. We study the case when the base ring has Krull dimension 0, and…

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

This paper explores the dimension theory of non-Noetherian graded rings by introducing the class of Hilbert-Serre rings. We generalize Krull's dimension theorem and Smoke's dimension theorem by establishing the fundamental inequalities…

For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x_1;\tau_1,\delta_1]...b[x_n;\tau_n,\delta_n] agrees with the PI degree of R[x_1;\tau_1]...b[x_n;\tau_n] when…

In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not…

We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to…

Given a complete, positively filtered ring $(R,f)$ and a compatible skew derivation $(\sigma,\delta)$, we may construct its skew power series ring $R[[x;\sigma,\delta]]$. Due to topological obstructions, even if $\delta$ is an \emph{inner}…