Related papers: An embedding problem of Noetherian rings into the …

In this paper, it is proved that a commutative noetherian local ring admitting a finitely generated module of finite projective and injective dimensions with respect to a semidualizing module is Gorenstein. This result recovers a celebrated…

We investigate homological and depth-theoretic properties of finitely generated modules of finite projective dimension over Noetherian local rings. A central theme is the study of criteria for freeness and reflexivity derived from the…

Let R* be an ideal-adic completion of a Noetherian integral domain R and let L be a subfield of the total quotient ring of R* such that L contains R. Let A denote the intersection of L with R*. The integral domain A sometimes inherits nice…

Let $R$ be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial…

In this paper, we introduce a new notion, called the integral dimension, for noetherian rings. It can be regarded as the weak Briancon-Skoda numbers of rings. The point is that every noetherian local ring has finite integral dimension.

Consider a Noetherian domain $R$ and a finite group $G \subseteq Gl_n(R)$. We prove that if the ring of invariants $R[x_1, \ldots, x_n]^G$ is a Cohen-Macaulay ring, then it is generated as an $R$-algebra by elements of degree at most…

We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a…

The main focus of this paper is on determining the highest non-vanishing local cohomology modules of \Omega_(B/R), \Omega_(B/V)(\Omega_(B/k)) where R is either a complete regular local ring or a complete local normal domain with coefficient…

Let $\mathcal{P}$ be the class of rings for which every indecomposable right module is pure-projective or pure-injective. When $R$ is a Noetherian local commutative ring of maximal ideal $P$, it is proven that $R\in\mathcal{P}$ if and only…

We give equivalences between given properties of a commutative ring, and other properties on its ring of Witt vectors. Amongst them, we characterise all commutative rings whose rings of Witt vectors are Noetherian. We define a new category…

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $X$ an arbitrary $R$--module. In this paper, for non-negative integers $s, t$ and a finitely…

We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give a thorough development of phi-modules…

We investigate two invariants of Noetherian semiperfect rings, namely the depth and a new invariant we call the "delooping level". These give lower and upper bounds for the finitistic dimension, respectively. As first theorems, we give a…

We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary abelian categories. The results are strongest for module categories of rngs with enough idempotents. We also reformulate the notion of Frobenius…

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to…

The notion of an Ohm-Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan-Hochster proof of Stillman's conjecture. As further restrictions are placed…

We study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantized Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained in [arXiv:0906.2930] for down-up…

This is a survey on the relation between homological properties of the Frobenius endomorphism and finiteness of various homological dimensions of the ring or of modules over it, such as global dimension and projective dimension. We begin…

By a theorem of Roberts, the integral closure of a regular local ring in a finite abelian extension of its fraction field is Cohen-Macaulay, provided that the degree of the extension is coprime to the characteristic of the residue field. We…

In this paper we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the results given in the literature.