Related papers: The ghost and weak dimensions of rings and ring sp…
The aim of this paper is the study of Gorenstein global and weak dimensions of semi-primary rings.
We motivate a relation between dark energy and the scale of new physics in weakly coupled string theory. This mixing between infrared and ultraviolet physics leads to a unique corner for real-world phenomenology: barring fine-tunings, we…
In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension and we study the weak Gorenstein homological…
We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimension. We also include the answer to a question of Y.~Xiang…
It is known that much of the structure of string theory can be derived from three-dimensional topological field theory and gravity. We show here that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in…
In this paper, we introduce and study the $S$-weak global dimension $S$-w.gl.dim$(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$. Moreover, commutative rings with $S$-weak global dimension at most $1$ are studied.…
The aim of this paper is to study the classical global and weak dimensions of the amalgamated duplication of a ring $R$ along a pure ideal $I$.
We study the Gorenstein weak global dimension of associative rings and its relation to the Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein weak global dimension is a left-right symmetric invariant --…
Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $\Gamma$. We first establish lower and upper bounds for the number of arcs in $\Gamma$ by using the diameter and weak metric…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes…
In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…
Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gaussian ring with nilradical $\mathcal{N} satisfying…
In this paper, the $\tau_q$-weak global dimension $\tau_q$-\cwd$(R)$ of a commutative ring $R$ is introduced. Rings with $\tau_q$-weak global dimension equal to $0$ are studied in terms of homologies, direct products, polynomial extensions…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields, describing traversable wormholes with flat and AdS asymptotics and regular black holes,…
We compute the Gorenstein weak dimension of a coherent power series rings over a commutative rings and we show that, in general, $\gwd(R) \leq 1$ does not imply that $R$ is an arithmetical ring.
We study the influence rules of the speckle size of light source on ghost imaging, and propose a new type of speckle patterns to improve the quality of ghost imaging. The results show that the image quality will first increase and then…
In this paper, we investigate the weak Gorenstein global dimensions. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GF-closed rings, that the left and…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
In the presence of large extra dimensions, the fundamental Planck scale can be much lower than the apparent four-dimensional Planck scale. In this setup, the weak gravity conjecture implies a much more stringent constraint on the UV cutoff…