Weak π-rings

In this paper we establish some characterizations for weak π-rings.     

On Litoff’s theorem

We give a short proof of Litoff’s theorem from the viewpoint of completely reducible modules.     

On primeness of general skew inverse Laurent series ring

Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x^?1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ.     

A canonical module characterization of Serre’s (R1)

In this short note, we give a characterization of domains satisfying Serre’s condition (R₁) in terms of their canonical modules. In the special case of toric rings, this generalizes a result of the second author [9 Yanagawa, K. (2015). Dualizing complexes of seminormal a?ne semigroup rings and toric face rings. J. Algebra 425:367–391.[Crossref], [Web of Science ®] , [Google Scholar]] where the normality is described in terms of the “shape” of the canonical module.     

On the inheritance of the strongly π-extending property

In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.     

Armendariz group rings

For a torsion or torsion-free group G and a field F, we characterize the group algebra FG that is Armendariz. Armendariz property for a group ring over a general ring R is also studied and related to those of Abelian group rings and the quaternion ring over R.     

Efficient and green oxidation of alcohols with tert-butyl hydrogenperoxide catalyzed by a recyclable magnetic core-shell nanoparticle-supported oxo-vanadium ephedrine complex

A novel method for the oxidation of alcohols to the corresponding carbonyl compounds has been successfully developed using tert-butyl hydrogenperoxide (TBHP) in the presence of a catalytic amount of recyclable magnetic nanoparticle-supported oxo-vanadium ephedrine complex (VO(ephedrine)₂@MNPs) in PEG as a green solvent at 80 °C. The catalyst can be magnetically recycled and successfully reused in six subsequent reaction cycles with only slight decreases of its catalytic activity.     

Theoretical assessment of structural,mechanical, and thermodynamic properties of Pd2Al

The physical properties, namely structural, mechanical, and thermodynamic properties, of Pd₂Al intermetallic compound were explored through first-principles calculations within the framework of density functional theory. The calculated lattice constants were consistent with the available experimental data. The calculated elastic constants revealed that Pd₂Al was mechanically stable. By the predicted elastic constants, several related properties, namely Cauchy pressures, shear anisotropy factors, directional Young's modulus, bulk, shear and Young's moduli, the ratio of K/G, Vickers hardness, sound velocity, and minimum thermal conductivity for Pd₂Al were evaluated. According to the calculated results, it was found that Pd₂Al possesses a highly anisotropic feature and behaves in a ductile manner with low stiffness. Finally, temperature-dependence of thermodynamic properties, namely Debye temperature and heat capacity, were also evaluated through the quasi-harmonic Debye model.