Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly rings and invertible discuss the relations between these several properties of rings. Also, study concept crossed products some defined product give relationship Moreover, in generalization for essential submodules, semi-uniform modules which is uniform modules.

objective: although coronary artery disease (cad) is the leading cause of death in type 2 diabetic patients, it is frequently asymptomatic. myocardial perfusion imaging (mpi) is reported to show ischemia in a significant number of asymptomatic diabetic patients. we studied the prevalence and severity of myocardial perfusion defects in asymptomatic diabetic patients and its clinical impact. meth...

Let $R$ be a commutative ring with identity‎. ‎A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$‎, ‎$a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...

An octahedral cobalt(III) complex, trans-[(Me2bpb)Co(bzlan)2]ClO4 (1), with H2Me2bpb = N,N’-(4,5-dimethyl-1,2-phenylene)dipicolinamide and bzlan = benzylamine, has been synthesized and characterized by elemental analyses, IR, UV-Vis, and 1H NMR spectroscopy. The structure of this complex has been determined by X-ray crystallography. The Me2bpb2– is a di-anionic tetradentate ligand furnishing a ...