Local dimension of trivial extension and amalgamation of rings

Local dimension is an ordinal valued invariant that is in some sense a measure of how far a ring is from being local and denoted [Formula: see text]. The purpose of this paper is to study the local dimension of ring extensions such as homomorphic image, trivial ring extension and the amalgamation of rings.

On Weakly S-Primary Ideals of Commutative Rings

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

Strongly ϕ-n-irreducible ideals

Let [Formula: see text] be a commutative ring, [Formula: see text] be an ideal of [Formula: see text], [Formula: see text] be a non-null positive integer and [Formula: see text] be a function where [Formula: see text] is the set of ideals of [Formula: see text]. In this paper, we define a new generalization of strongly [Formula: see text]-irreducible ideals called strongly [Formula: see text]-[Formula: see text]-irreducible ideal, that is, whenever [Formula: see text] and [Formula: see text] for [Formula: see text] ideals of [Formula: see text], then there are [Formula: see text] of the [Formula: see text]’s whose intersection is in [Formula: see text]. We study the stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal.

Cancellation ideals of a ring extension

We study properties of cancellation ideals of ring extensions. Let R⊆S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R⊆S if whenever IB=IC for two S-regular (finitely generated) R-submodules B and C of S, then B=C. We show that a finitely generated ideal I is a cancellation ideal of the ring extension R⊆S if and only if I is S-invertible.

Extension velocity limiter for the ring of an elastically adaptive peripheral docking mechanism

The docking ring of an elastically adaptive docking mechanism on the initial contact signal is extended by spring-loaded mechanisms of the rods in order to improve capture conditions. In the process, it reaches a high velocity, which applies unacceptably high impact loads to the docking interface. This paper discusses an extension velocity limiter for the docking ring, its analytical model, and a brief procedure for calculating its parameters. It describes a simplified model for ring extension during initial contact, and a method for determining viscous friction coefficient of the ball-screw pair of the docking mechanism, which is a parameter in the model. It presents the procedure, results and comparison of simulations of the docking ring extension both with the use of the proposed retarder and without it. It is demonstrated that the use of the velocity limiter permits to meet the requirements of the International Standard for pulsed loads on the passive interface. The paper describes a design option for velocity limiter that has acceptable mass and dimensions. Keywords: spacecraft docking, elastically adaptive docking mechanism, retraction device, velocity limiter, mechanical governor

On partial skew groupoid rings

Given a partial action [Formula: see text] of a connected groupoid [Formula: see text] on an associative ring [Formula: see text] we investigate under what conditions the partial skew groupoid ring [Formula: see text] can be realized as a partial skew group ring. In such a case, applications concerning to the separability, semisimplicity and Frobenius property of the ring extension [Formula: see text] as well as to the artinianity of [Formula: see text] are given.

On Nonnil-S-Noetherian Rings

Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

Structural Isomerism and Enhanced Lipophilicity of Pyrithione Ligands of Organoruthenium(II) Complexes Increase Inhibition on AChE and BuChE

The increasing number of Alzheimer’s disease (AD) cases requires the development of new improved drug candidates, possessing the ability of more efficient treatment as well as less unwanted side effects. Cholinesterase enzymes are highly associated with the development of AD and thus represent important druggable targets. Therefore, we have synthesized eight organoruthenium(II) chlorido complexes 1a–h with pyrithione-type ligands (pyrithione = 1-hydroxypyridine-2(1H)-thione, a), bearing either pyrithione a, its methyl (b-e) or bicyclic aromatic analogues (f–h) and tested them for their inhibition towards electric eel acetylcholinesterase (eeAChE) and horse serum butyrylcholinesterase (hsBuChE). The experimental results have shown that the novel complex 1g with the ligand 1-hydroxyquinoline-2-(1H)-thione (g) improves the inhibition towards eeAChE (IC50 = 4.9 μM) and even more potently towards hsBuChE (IC50 = 0.2 μM) in comparison with the referenced 1a. Moreover, computational studies on Torpedo californica AChE have supported the experimental outcomes for 1g, possessing the lowest energy value among all tested complexes and have also predicted several interactions of 1g with the target protein. Consequently, we have shown that the aromatic ring extension of the ligand a, though only at the appropriate position, is a viable strategy to enhance the activity against cholinesterases.