Ore Extension Rings Satisfy the Weak PS-Rings

The main result of this paper is that: If R is a weak right PS-ring, then A = R[x; α, δ], the Ore extension ring, is a weak right PS-ring whenever the following conditions hold on R is an (α, δ)-compatible NI-ring with nil(R) nilpotent, α(e) = e and δ(e) = 0 for every idempotent e ∈ R.

Validation of iterative CT reconstruction by inter and intra observer performance assessment of artificial lung foci

We investigate the suitability of statistical and model-based iterative reconstruction (IR) algorithm strengths and their influence on image quality and diagnostic performance in low-dose computer tomography (CT) protocols for lung-cancer screening procedures. We evaluate the inter- and intra-observer performance for the assessment of iterative CT reconstruction. Artificial lung foci shaped as spheres and spicules made from material with calibrated Hounsfield units were pressed within layered granules in lung lobes of an anthropomorphic phantom. Adaptively, a soft-tissue- and fat- extension ring were attached. The phantom with foci was scanned using standard high contrast, low-dose and ultra lowdose protocols. For reconstruction the IR algorithm ADMIRE at four different strength levels were used. Two ranking tests and Friedman statistics were performed. Fleiss k and modified Cohen’s kneywere used to quantify inter- and intra-observer performance. In conjunction with the standard lung kernel BL75 radiologists evaluated medium to high IR strength, with preference to S4, as suitable for lung foci detection. When varying reconstruction kernels the ranking became more random than with varying phantom diameter. The inter-observer reliability shows poor to slight agreement expressed by k<0 and k=0-0.20 . For the intra-observer reliability non- agreement with kney=0-0.20and moderate agreement with kney=0.60-0.79 for the first ranking test, and almost perfect agreement with kney>0.90 for the second ranking test was observed. In conclusion, our validation suggests radiological preference of medium to high iteration strengths, especially S4, for lung foci detection. An investigation of the correlation between diagnostic experience and the subjective perception of IR reconstructed CT images still needs to be investigated.

The Category of Modules on an n-Trivial Extension: the Basic Properties

In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) n-trivial extension of a category by a family of endofunctors. Among other results, projective, injective and flat objects of this category are characterized, and two applications are presented at the end of this paper. We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.

Wakamatsu tilting modules over ring extension

For a ring [Formula: see text], an extension ring [Formula: see text], and a fixed right [Formula: see text]-module [Formula: see text], we prove the induced left [Formula: see text]-module [Formula: see text] is a Wakamatsu tilting module when [Formula: see text] is a Wakamatsu tilting module.

Some types of ring elements in Ore extensions over noncommutative rings

Let [Formula: see text] be an associative unital ring with an endomorphism [Formula: see text] and [Formula: see text]-derivation [Formula: see text]. Some types of ring elements such as the units and the idempotents play distinguished roles in noncommutative ring theory, and will play a central role in this work. In fact, we are interested to study the unit elements, the idempotent elements, the von Neumann regular elements, the [Formula: see text]-regular elements and also the von Neumann local elements of the Ore extension ring [Formula: see text], when the base ring [Formula: see text] is a right duo ring which is [Formula: see text]-compatible. As an application, we completely characterize the clean elements of the Ore extension ring [Formula: see text], when the base ring [Formula: see text] is a right duo ring which is [Formula: see text]-compatible.

On Ore extension and skew power series rings with some restrictions on zero-divisors

The study of rings with right Property ([Formula: see text]), has done an important role in noncommutative ring theory. Following literature, a ring [Formula: see text] has right Property ([Formula: see text]) if every finitely generated two-sided ideal consisting entirely of left zero-divisors has a nonzero right annihilator. Our results in this paper concerns the right Property ([Formula: see text]) of Ore extensions as well as skew power series rings. We will show that if [Formula: see text] is a right duo ring, then the skew power series ring [Formula: see text] has right Property ([Formula: see text]), when [Formula: see text] is right Noetherian and [Formula: see text]-compatible. Moreover, for a right duo ring [Formula: see text] which is [Formula: see text]-compatible, it is shown that (i) the Ore extension ring [Formula: see text] has right Property ([Formula: see text]) and (ii) [Formula: see text] is right zip if and only if [Formula: see text] is right zip. As a corollary of our results, we provide answers to some open questions related to Property [Formula: see text], raised in [C. Y. Hong, N. K. Kim, Y. Lee and S. J. Ryu, Rings with Property ([Formula: see text]) and their extensions, J. Algebra 315 (2007) 612–628].

Reducing Solid Particle Erosion on Steam Turbine Stages

Solid Particle Erosion (SPE) damage can be found on steam turbine stages. These solid particles are caused by the exfoliation of iron oxides formed on the inner surfaces of both boiler tubes and steam pipes which are exposed to elevated temperature. They can damage both fixed and Moving Blades, as well as both outer extension ring and tip seals. Severe SPE damages can be expensive for the utility industry due to reduced efficiency and lost power generation, as well as increased costs of repair or replacement of eroded components. Thus it is very important to understand this phenomenon and propose cost effective solutions to reduce the damage. This study investigates the effects of SPE damage using particle trajectory calculations. This investigation confirms that “Bounce Back” is the dominant cause for the SPE damage on both Fixed Blade trailing edge and Moving Blade leading edge. The particles do not accelerate at same speed as steam, therefore they travel much slower when they hit the Moving Blade leading edge. Then they are thrown back towards the Fixed Blade to hit the trailing edge. Due to strong centrifugal forces, the particles are also thrown radically outwards and damage both outer extension ring and tip seals. Based on these enhanced understandings, a practical solution is proposed to reduce SPE damage. It is predicted to have negligible impact on the stage performance. Evidence from the latest inspection demonstrates that this solution is very effective in reducing SPE damage to the Fixed Blade trailing edge.

Existence Of Coefficient Subring for Transcendental Extension Ring

As a consequence of Cohen's structure Theorem for complete local rings that every _nite commutative ring R of characteristic pn contains a unique special primary subring R0 satisfying R/J(R) = R0/pR0: Cohen called R0 the coe_cient subring of R. In this paper we will study the case when the ring is a transcendental extension local artinian duo ring R; we proved that even in this case R will has a commutative coe_cient subring.

Units on the Gauss extension of a Galois ring

Ring extensions are a well-studied topic in ring theory. In this paper, we study the structure of the Gauss extension of a Galois ring. We determine the structures of the extension ring and its unit group.

Costar modules, r-Costar modules over ring extensions

For a ring A, an extension ring B, and a fixed right A-module M, we prove that M is costar module, r-costar module if and only if the induced module Hom A(B,M) is costar module, r-costar module respectively.