Correspondences of Coclosed Submodules

We establish an order-preserving bijective correspondence between the sets of coclosed elements of some bounded lattices related by suitable Galois connections. As an application, we deduce that if M is a finitely generated quasi-projective left R-module with S = End _R (M) and N is an M-generated left R-module, then there exists an order-preserving bijective correspondence between the sets of coclosed left R-submodules of N and coclosed left S-submodules of Hom _R (M, N).     

Some preserving sandwich results of certain integral operators on multivalent meromorphic functions

In this paper, we obtain some subordination, superordination and sandwich-preserving results of a certain integral operator on p-valent meromorphic functions.     

GC-MS analysis of ring and side chain regioisomers of ethoxyphenethylamines

Mass spectral differentiation of 3,4-methylenedioxymethamphetamine (3,4-MDMA), a controlled drug, and its 2,3-regioisomer from the ring substituted ethoxyphenethylamines is possible after formation of the perfluoroacyl derivatives, pentafluoropropionamides (PFPA), and heptafluorobutyrylamides (HFBA). The ring substituted ethoxyphenethylamines constitute a unique set of compounds having an isobaric relationship with 3,4-MDMA. These isomeric forms of the 2-, 3-, and 4-ethoxy phenethylamines have mass spectra essentially equivalent to 3,4-MDMA; all have molecular weight of 193 and major fragment ions in their electron ionization mass spectra at m/z 58 and 135/136. All the side chain regioisomers of 2-ethoxy phenethylamine having equivalent mass spectra to 3,4-MDMA are synthesized and compared via gas chromatography-mass spectrometry to 2,3- and 3,4-methylenedioxymethamphetamine. The mass spectra for the perfluoroacyl derivatives of the primary and secondary amine regioisomers are significantly individualized, and the side chain regioisomers yield unique hydrocarbon fragment ions at m/z 148, 162, and 176. Additionally, the substituted ethoxymethamphetamines are distinguished from the methylenedioxymethamphet-amines via the presence of the m/z 107 ion. Gas chromatographic separation on relatively non-polar stationary phases successfully resolves these derivatives.     

On weakly nil-clean rings

We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring \(\mathbb{M}_n (R)\) is weakly nil-clean, and to show that the endomorphism ring End _D (V) over a vector space V _D is weakly nil-clean if and only if it is nil-clean or dim(V) = 1 with D?= ?₃.     

A new and facile tetrachlorosilane-promoted one-pot condensation for the synthesis of a novel series of tetracyclic 1,5-thiazepines

A new and facile approach for the one-pot synthesis of a novel series of tetracyclic 1,5-thiazepines is described. The reaction occurs through cyclocondensation of fused cyclic ketones, aromatic aldehydes, and 2-aminothiophenol using tetrachlorosilane as a promoter in methylene chloride at ambient temperature.