On reduced rings with prime factors simple

We obtain a common generalization of the results by Wong and Birkenmeier-Kim-Park, respectively, which say that a reduced ring with unity is strongly (respectively, weakly) regular if and only if all of its prime homomorphic images are division rings (respectively, simple domains). Our arguments are different from those in the known proofs and are quite simple. They also give a characterization of weakly regular reduced rings without unity. This characterization implies in particular that the class of weakly regular reduced rings forms a radical class. However, even if a weakly regular reduced ring has no unity, its prime homomorphic images must be simple domains with unity. In the second part of the paper, we study reduced rings whose prime homomorphic images are simple domains (not necessarily with unity).

Rings with Boolean Lattices of One-Sided Annihilators

The present paper is part of the research on the description of rings with a given property of the lattice of left (right) annihilators. The anti-isomorphism of lattices of left and right annihilators in any ring gives some kind of symmetry: the lattice of left annihilators is Boolean (complemented, distributive) if and only if the lattice of right annihilators is such. This allows us to restrict our investigations mainly to the left side. For a unital associative ring R, we prove that the lattice of left annihilators in R is Boolean if and only if R is a reduced ring. We also prove that the lattice of left annihilators of R being two-sided ideals is complemented if and only if this lattice is Boolean. The last statement, in turn, is known to be equivalent to the semiprimeness of R. On the other hand, for any complete lattice L, we construct a nilpotent ring whose lattice of left annihilators coincides with its sublattice of left annihilators being two-sided ideals and is isomorphic to L. This construction shows that the assumption of R being unital cannot be dropped in any of the above two results. Some additional results on rings with distributive or complemented lattices of left annihilators are obtained.

Effect of interventional edge-to-edge repair in tricuspid regurgitation on ring dimensions

Background The concept of percutaneous tricuspid valve edge-to-edge repair (pTVR) is based on the connection of leaflets in the area of insufficiency using a coaptation device. By closing the coaptation device a considerable tractive force is applied on the leaflets, which might have an effect on the valve ring. Aim of the study was to examine the impact of device implantation on tricuspid ring dimensions. Methods During pTVR 3D zoom loops of tricuspid valve were acquired before and after clip placement using transoesophageal echocardiography. Measurements of TV ring dimensions included the following parameters: ring area (TV area), maximal diameter, minimal diameter, eccentricity index (Figure 1). Tenting area was derived from a four-chamber view of the valve. In addition, regurgitation severity was graded from 1+ to 5+ by measuring vena contracta area (VCA3D) in 3D full volume colour Doppler loop using multiplanar reconstruction. Right atrial (RA) and ventricular volumes (RVVd3D, RVVs3D) and function (RVEF3D) were assessed in a 3D full volume loop. Results The study population comprised 97 patients (age 78±6 years, 47 male), who underwent pTVR at our hospital. As expected cavity dimension correlated with TV area size (for RVVd3D r=0.51, p<0.001 and for RA volume r=0.71, p<0.001). The mean TV ring area was significantly reduced (ring area 8.53±2.23 cm2/m2BSA vs. 7.55±2.18 cm2/m2BSA, p<0.001) and the ring shape became more oval (Eccentricity index 1.2±0.15 vs. 1.29±0.17, p<0.001) after pTVR. The reduction of ring area (12±7%, range 0.7–28%) showed an only modest correlation to the number of implanted coaptation devices (r=0.30, p<0.001) and percentage reduction of VCA3D (r=0.36, p<0.001). In the patient group with a ring area change ≥12% a reduction to TR grade ≤2+ by pTVR was achieved in 83% of cases, whereas only 62% of patients reached moderate TR when area change was below 12%. Conclusion pTVR using coaptation devices reduces the ring area. This effect is related to the number of devices implanted. FUNDunding Acknowledgement Type of funding sources: None.

Notes on the zero-divisor graph and annihilating-ideal graph of a reduced ring

We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dt t (𝔸𝔾 (R)) = |ℬ(R)| and also if in addition |Min(R)| > 2, then dt(𝔸𝔾 (R)) = |ℬ (R)|. Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dt t (𝔸𝔾 (R)) is finite if and only if Min(R) is finite.

A nilpotency criterion for derivations over reduced ℚ-algebras

Let [Formula: see text] be a reduced ring containing [Formula: see text] and let [Formula: see text] be commuting locally nilpotent derivations of [Formula: see text]. In this paper, we give an algorithm to decide the local nilpotency of derivations of the form [Formula: see text], where [Formula: see text] are elements in [Formula: see text].

Development and validation of an in silico decision-tool to guide optimisation of intravenous artesunate dosing regimens for severe falciparum malaria patients

Most deaths from severe falciparum malaria occur within 24 hours of presentation to hospital. Intravenous (i.v.) artesunate is the first-line treatment for severe falciparum malaria, but its efficacy may be compromised by delayed parasitological responses. In patients with severe malaria the life-saving benefit of the artemisinin derivatives is their ability to clear circulating parasites rapidly, before they can sequester and obstruct the microcirculation. To evaluate the dosing of i.v. artesunate for the treatment of artemisinin-sensitive and reduced ring stage sensitivity to artemisinin severe falciparum malaria infections Bayesian pharmacokinetic-pharmacodynamic modelling of data from 94 patients with severe malaria (80 children from Africa and 14 adults from Southeast Asia) was performed. Assuming delayed parasite clearance reflects a loss of ring stage sensitivity to artemisinin derivatives, the median (95% credible interval) percentage of patients clearing ≥99% parasites within 24 hours (PC24≥99%) for standard (2.4 mg/kg i.v. artesunate at 0 and 12 hours) and simplified (4 mg/kg i.v. artesunate at 0 hours) regimens were 65% (52.5%-74.5%) versus 44% (25%-61.5%) for adults, 62% (51.5%-74.5%) versus 39% (20.5%-58.5%) for larger children (≥20 kg) and 60% (48.5%-70%) versus 36% (20%-53.5%) for smaller children (<20 kg). The upper limit of the credible intervals for all regimens was below a PC24≥99% of 80%, a threshold achieved on average in clinical studies of severe falciparum malaria infections. Rapid clearance of parasites, where there is loss of ring stage sensitivity to artemisinin, in patients with severe falciparum malaria is compromised with the currently recommended and proposed simplified i.v. artesunate dosing regimens.

On reduced archimedean skew power series rings

In this paper, we prove that if [Formula: see text] is an Archimedean reduced ring and satisfy ACC on annihilators, then [Formula: see text] is also an Archimedean reduced ring. More generally, we prove that if [Formula: see text] is a right Archimedean ring satisfying the ACC on annihilators and [Formula: see text] is a rigid automorphism of [Formula: see text], then the skew power series ring [Formula: see text] is right Archimedean reduced ring. We also provide some examples to justify the assumptions we made to obtain the required result.

The reduced ring order and lower semi-lattices II

This paper continues the study of the reduced ring order (rr-order) in reduced rings where [Formula: see text] if [Formula: see text]. A reduced ring is called rr-good if it is a lower semi-lattice in the order. Examples include weakly Baer rings (wB or PP-rings) but many more. Localizations are examined relating to this order as well as the Pierce sheaf. Liftings of rr-orthogonal sets over surjections of reduced rings are studied. A known result about commutative power series rings over wB rings is extended, via methods developed here, to very general, not necessarily commutative, power series rings defined by an ordered monoid, showing that they are wB.