Catalyst-free grinding method: a new avenue for synthesis of 6-amino-3-methyl-4-aryl-1H-pyrazolo[3,4-b]pyridine-5-carbonitrile and DFT studies on the mechanistic pathway of this category of compounds

Research on Chemical Intermediates - A novel, efficient, one-pot, catalyst-free grinding procedure for synthesis of 6-amino-3-methyl-4-aryl-1H-pyrazolo[3,4-b]pyridine-5-carbonitrile is reported....     

Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R,\mathfrak{m})}$ be a local ring, and let C be a semidualizing R-module. In this paper, we are concerned with the C-injective and G _C -injective dimensions of certain local cohomology modules of R. Firstly, the injective dimension of C and the above quantities are compared. Secondly, as an application of the above comparisons, a characterization of a dualizing module of R is given. Finally, it is shown that if R is Cohen-Macaulay of dimension d such that ${\rm H}_{\mathfrak{m}}^{d}(C)$ is C-injective, then R is Gorenstein. This is an answer to a question which was recently raised.